Bibliography G
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Evaluation of
-gamma function and -analogues by iterative algorithms,Numer. Algorithms 49 (1-4), pp. 159–168.
- External Links:
- ISSN 1017-1398, Document, FullText, MathReview (Necdet Batir), ZentralBlatt.
- Referenced by:
- §17.18, §17.18, §5.21, §5.21.
- Encodings:
- BibTeX
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A new application of the discrete Laguerre polynomials in the numerical evaluation of the Hankel transform of a strongly decreasing even function,J. Comput. Phys. 42 (2), pp. 277–287.
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On high precision methods for computing integrals involving Bessel functions,Math. Comp. 33 (147), pp. 1049–1057.
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- ¶ ‣ §10.74(vii).
- Encodings:
- BibTeX
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On the generalization of a method for computing Bessel function integrals,J. Comput. Appl. Math. 6 (2), pp. 167–168.
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- Referenced by:
- ¶ ‣ §10.74(vii).
- Encodings:
- BibTeX
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Sur les équations différentielles du second ordre et du premier degré dont l’intégrale générale est a points critiques fixes,Acta Math. 33 (1), pp. 1–55.
- External Links:
- ISSN 0001-5962, Document, MathReview Entry, ZentralBlatt.
- Referenced by:
- §32.10(ii), §32.10(iv), §32.7(ii).
- Encodings:
- BibTeX
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The GAP Group, Centre for Interdisciplinary Research in Computational Algebra, University of St. Andrews, United Kingdom..
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A continued fraction algorithm for the computation of higher transcendental functions in the complex plane,Math. Comp. 21 (97), pp. 18–29.
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- Referenced by:
- §10.74(v), ¶ ‣ §3.10(ii).
- Encodings:
- BibTeX
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Basic Hypergeometric Series,Second edition, Encyclopedia of Mathematics and its Applications, Vol. 96, Cambridge University Press, Cambridge.
- Notes:
- With a foreword by Richard Askey
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- ISBN 0-521-83357-4, MathReview (Shaun Cooper), ZentralBlatt.
- Referenced by:
- §17.1, §17.10, §17.13, §17.16, §17.4(i), §17.5, §17.6(i), §17.6(ii), §17.6(iii), §17.6(iv), §17.6(v), §17.7(i), §17.7(ii), §17.7(iii), §17.8, §17.9(i), §17.9(ii), §17.9(iii), Ch.17, §18.27(i), §18.27(ii), §18.27(iii), §18.27(iv), §18.28(i), §18.28(ii), §18.28(v), §18.28(viii), §26.19.
- Encodings:
- BibTeX
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An inequality of Turán type for Jacobi polynomials,Proc. Amer. Math. Soc. 32, pp. 435–439.
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- Referenced by:
- §18.14(ii).
- Encodings:
- BibTeX
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Formulas of the Dirichlet-Mehler Type,in Fractional Calculus and its Applications,Lecture Notes in Math., Vol. 457, pp. 207–215.
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- MathReview (Mourad E. H. Ismail), ZentralBlatt.
- Referenced by:
- ¶ ‣ §18.10(i).
- Encodings:
- BibTeX
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Orthogonality of certain functions with respect to complex valued weights,Canad. J. Math. 33 (5), pp. 1261–1270.
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- ISSN 0008-414X, MathReview (Mourad E. H. Ismail), ZentralBlatt.
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- §18.33(v).
- Encodings:
- BibTeX
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New inequalities for the zeros of Jacobi polynomials,SIAM J. Math. Anal. 18 (6), pp. 1549–1562.
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- ISSN 0036-1410, Document, MathReview (E. Riekstiņš), ZentralBlatt.
- Referenced by:
- §18.16(ii), §18.16(vi).
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- BibTeX
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New inequalities for the zeros of confluent hypergeometric functions,in Asymptotic and computational analysis (Winnipeg, MB, 1989),pp. 175–192.
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Asymptotics and bounds for the zeros of Laguerre polynomials: A survey,J. Comput. Appl. Math. 144 (1-2), pp. 7–27.
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- Referenced by:
- ¶ ‣ §18.16(iv), §18.16(iv), §18.16(vi).
- Encodings:
- BibTeX
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La fonction d’onde de Bethe,Masson, Paris (French).
- External Links:
- ISBN 2-225-79607-6, MathReview (John H. Lowenstein), ZentralBlatt.
- Referenced by:
- §31.17(i).
- Encodings:
- BibTeX
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The triplets of helium,Philos. Trans. Roy. Soc. London Ser. A 228, pp. 151–196.
- External Links:
- Document, ZentralBlatt (Möglich, Dr. F.).
- Referenced by:
- §34.3(vii).
- Encodings:
- BibTeX
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Werke. Band II,pp. 436–447 (German).
- Notes:
- Reprinted by Georg Olms Verlag, Hildesheim, 1973.
- External Links:
- FullText, MathReview, ZentralBlatt.
- Referenced by:
- §27.2(i).
- Encodings:
- BibTeX
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Algorithm 222: Incomplete beta function ratios,Comm. ACM 7 (3), pp. 143–144.
- Notes:
- Variable-precision Algol program. For a Certification see same journal 7 (1964), p. 244.
- External Links:
- ISSN 0001-0782, Document, Certification.
- Referenced by:
- §8.28(iv).
- Encodings:
- BibTeX
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Algorithm 236: Bessel functions of the first kind,Comm. ACM 7 (8), pp. 479–480.
- Notes:
- For certification see same journal 8(1965), pp. 105–106, for remark see ACM Trans. Math. Software, 1(1975), pp. 282–284. Includes Algol program, maximum accuracy: 11D.
- External Links:
- ISSN 0001-0782, Document.
- Referenced by:
- §10.77(iii).
- Encodings:
- BibTeX
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Algorithm 259: Legendre functions for arguments larger than one,Comm. ACM 8 (8), pp. 488–492.
- Notes:
- Variable-precision Algol. For remark see ACM Trans. Math. Software 3(2) (1977), p. 204–205
- External Links:
- ISSN 0001-0782, Document.
- Referenced by:
- §14.34(ii).
- Encodings:
- BibTeX
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Algorithm 292: Regular Coulomb wave functions,Comm. ACM 9 (11), pp. 793–795.
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Algorithm 363: Complex error function,Comm. ACM 12 (11), pp. 635.
- Notes:
- Includes Algol program, maximum accuracy 10S. For certification see same journal v. 15 (1972), pp. 465–466
- External Links:
- ISSN 0001-0782, Document.
- Referenced by:
- §7.25(iii).
- Encodings:
- BibTeX
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Algorithm 471: Exponential integrals,Comm. ACM 16 (12), pp. 761–763.
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Evaluation of the repeated integrals of the coerror function,ACM Trans. Math. Software 3, pp. 240–252.
- Notes:
- For software see Gautschi (1977b).
- External Links:
- ISSN 0098-3500, Document, ZentralBlatt.
- Referenced by:
- §7.22(iii).
- Encodings:
- BibTeX
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Algorithm 521: Repeated integrals of the coerror function,ACM Trans. Math. Software 3, pp. 301–302.
- Notes:
- Single-precision Fortran, maximum accuracy 14D
- External Links:
- ISSN 0098-3500, Document, TOMS module 521 (in GAMS).
- Referenced by:
- §7.25(ii), W. Gautschi (1977a).
- Encodings:
- BibTeX
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Algorithm 542: Incomplete gamma functions,ACM Trans. Math. Software 5 (4), pp. 482–489.
- Notes:
- Single-precision Fortran.
- External Links:
- ISSN 0098-3500, Document, TOMS module 542 (in GAMS), ZentralBlatt.
- Referenced by:
- §8.28(ii).
- Encodings:
- BibTeX
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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules,ACM Trans. Math. Software 20 (1), pp. 21–62.
- Notes:
- For remark see same journal 24(1998), p. 355.
- External Links:
- Document, ISSN 0098-3500, TOMS module 726 (in GAMS), ZentralBlatt.
- Referenced by:
- §18.42, §3.5(v), §3.5(v).
- Encodings:
- BibTeX
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On the computation of modified Bessel function ratios,Math. Comp. 32 (143), pp. 865–875.
- External Links:
- ISSN 0025-5718, FullText, MathReview (James M. Horner), ZentralBlatt.
- Referenced by:
- §10.74(v).
- Encodings:
- BibTeX
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Exponential integral
for large values of 
,J. Res. Nat. Bur. Standards 62, pp. 123–125.- External Links:
- MathReview (W. Wasow), ZentralBlatt.
- Referenced by:
- §8.11(iii), §8.11(iii), §8.20(ii).
- Encodings:
- BibTeX
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Some elementary inequalities relating to the gamma and incomplete gamma function,J. Math. Phys. 38 (1), pp. 77–81.
- External Links:
- MathReview (H. O. Pollak), ZentralBlatt.
- Referenced by:
- §5.6(i), §6.8, §7.8, §8.10.
- Encodings:
- BibTeX
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Recursive computation of the repeated integrals of the error function,Math. Comp. 15 (75), pp. 227–232.
- External Links:
- FullText, MathReview (J. C. P. Miller), ZentralBlatt.
- Referenced by:
- §7.22(iii).
- Encodings:
- BibTeX
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Computational aspects of three-term recurrence relations,SIAM Rev. 9 (1), pp. 24–82.
- External Links:
- Document, MathReview (E. Frank), ZentralBlatt.
- Referenced by:
- §10.74(iv), §14.32, ¶ ‣ §3.10(iii), §3.6(iii).
- Encodings:
- BibTeX
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Efficient computation of the complex error function,SIAM J. Numer. Anal. 7 (1), pp. 187–198.
- External Links:
- Document, MathReview (P. Barrucand), ZentralBlatt.
- Referenced by:
- §7.22(i), §7.25(iii).
- Encodings:
- BibTeX
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A harmonic mean inequality for the gamma function,SIAM J. Math. Anal. 5 (2), pp. 278–281.
- External Links:
- Document, MathReview (S. Saran), ZentralBlatt.
- Referenced by:
- §5.6(i).
- Encodings:
- BibTeX
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Computational Methods in Special Functions – A Survey,in Theory and Application of Special Functions (Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975),pp. 1–98. Math. Res. Center, Univ. Wisconsin Publ., No. 35.
- External Links:
- MathReview (H. E. Fettis), ZentralBlatt.
- Referenced by:
- ¶ ‣ §19.36(ii), §19.5.
- Encodings:
- BibTeX
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A computational procedure for incomplete gamma functions,ACM Trans. Math. Software 5 (4), pp. 466–481.
- External Links:
- ISSN 0098-3500, Document, ZentralBlatt.
- Referenced by:
- §8.25(iv), §8.25(v).
- Encodings:
- BibTeX
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Un procedimento di calcolo per le funzioni gamma incomplete,Rend. Sem. Mat. Univ. Politec. Torino 37 (1), pp. 1–9 (Italian).
- External Links:
- MathReview (C. Dagnino), ZentralBlatt.
- Referenced by:
- ¶ ‣ §3.10(iii).
- Encodings:
- BibTeX
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How and how not to check Gaussian quadrature formulae,BIT 23 (2), pp. 209–216.
- External Links:
- ISSN 0006-3835, Document, MathReview (G. A. Evans), ZentralBlatt.
- Referenced by:
- §3.5(v), §9.17(iii).
- Encodings:
- BibTeX
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Questions of Numerical Condition Related to Polynomials,in Studies in Numerical Analysis,pp. 140–177.
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On the computation of generalized Fermi-Dirac and Bose-Einstein integrals,Comput. Phys. Comm. 74 (2), pp. 233–238.
- External Links:
- ISSN 0010-4655, Document, MathReview, ZentralBlatt.
- Referenced by:
- §25.12(iii), §25.18(i), §25.21(vii).
- Encodings:
- BibTeX
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Orthogonal Polynomials: Applications and Computation,in Acta Numerica, 1996,Acta Numerica, Vol. 5, pp. 45–119.
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Numerical Analysis. An Introduction,Birkhäuser Boston Inc., Boston, MA.
- External Links:
- ISBN 0-8176-3895-4, MathReview (Ian Gladwell), ZentralBlatt.
- Referenced by:
- ¶ ‣ §3.11(v), §3.11(v), ¶ ‣ §3.8(iii), §3.8(ii), §3.8(vii), Ch.3.
- Encodings:
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The Computation of Special Functions by Linear Difference Equations,in Advances in Difference Equations (Veszprém, 1995),(I. Győri and G. Ladas Eds.), pp. 213–243.
- External Links:
- ISBN 90-5699-521-9, MathReview, ZentralBlatt.
- Referenced by:
- §3.6(iii), §3.6(vii).
- Encodings:
- BibTeX
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The incomplete gamma functions since Tricomi,in Tricomi’s Ideas and Contemporary Applied Mathematics (Rome/Turin, 1997),Atti Convegni Lincei, Vol. 147, pp. 203–237.
- External Links:
- FullText, MathReview (Richard B. Paris), ZentralBlatt.
- Referenced by:
- Ch.8.
- Encodings:
- BibTeX
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A note on the recursive calculation of incomplete gamma functions,ACM Trans. Math. Software 25 (1), pp. 101–107.
- External Links:
- ISSN 0098-3500, Document, MathReview Entry, ZentralBlatt.
- Referenced by:
- §8.25(v).
- Encodings:
- BibTeX
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Computation of Bessel and Airy functions and of related Gaussian quadrature formulae,BIT 42 (1), pp. 110–118.
- External Links:
- ISSN 0006-3835, Document, MathReview (Khélifa Trimèche), ZentralBlatt.
- Referenced by:
- §10.74(iii), §9.17(iii).
- Encodings:
- BibTeX
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Gauss quadrature approximations to hypergeometric and confluent hypergeometric functions,J. Comput. Appl. Math. 139 (1), pp. 173–187.
- External Links:
- ISSN 0377-0427, Document, MathReview (Hasan Taşeli), ZentralBlatt.
- Referenced by:
- §13.29(iii), §15.19(iii).
- Encodings:
- BibTeX
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Orthogonal Polynomials: Computation and Approximation,Numerical Mathematics and Scientific Computation, Oxford University Press, New York.
- Notes:
- OPQ, a package of Matlab routines for generating classical and Sobolev orthogonal polynomials, accompanies this book.
- External Links:
- OPQ, ISBN 0-19-850672-4, MathReview Entry, ZentralBlatt.
- Referenced by:
- §18.40, §18.42, §3.5(v).
- Encodings:
- BibTeX
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Elastic scattering of photons by a hydrogen atom,Phys. Rev. 163 (1), pp. 147–155.
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A table of integrals of the exponential integral,J. Res. Nat. Bur. Standards Sect. B 73B, pp. 191–210.
- External Links:
- MathReview (John Todd), ZentralBlatt.
- Referenced by:
- §6.14(iii), §6.17, §6.7(iv).
- Encodings:
- BibTeX
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A table of integrals of the error function. II. Additions and corrections,J. Res. Nat. Bur. Standards Sect. B 75B, pp. 149–163.
- Notes:
- See for the first part same journal, Sect. B 73, 1-20 (1969)
- External Links:
- MathReview, ZentralBlatt.
- Referenced by:
- §7.14(iii).
- Encodings:
- BibTeX
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Generalized Functions. Vol. 1: Properties and Operations,Academic Press, New York.
- Notes:
- Translated from the Russian by Eugene Saletan. A paperbound reprinting by the same publisher appeared in 1977
- External Links:
- MathReview, ZentralBlatt.
- Referenced by:
- §2.6(i).
- Encodings:
- BibTeX
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Die Beugung einer ebenen elektromanetischen Welle an zwei parallelen unendlich langen idealleitenden Zylindern von elliptischem Querschnitt,Ann. Physik (7) 468, pp. 237–251 (German).
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WKB and turning point theory for second-order difference equations,in Spectral Methods for Operators of Mathematical Physics,Oper. Theory Adv. Appl., Vol. 154, pp. 101–138.
- External Links:
- FullText, MathReview (Ioannis K. Purnaras), ZentralBlatt.
- Referenced by:
- §18.15(v), §18.15(v).
- Encodings:
- BibTeX
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Some integrals involving three Bessel functions when their arguments satisfy the triangle inequalities,J. Math. Phys. 25 (11), pp. 3350–3356.
- External Links:
- ISSN 0022-2488, Document, MathReview (B. R. Bhonsle), ZentralBlatt.
- Referenced by:
- ¶ ‣ §10.22(iv), §10.43(iv).
- Encodings:
- BibTeX
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Integrals of three Bessel functions and Legendre functions. I,J. Math. Phys. 26 (4), pp. 633–644.
- External Links:
- ISSN 0022-2488, Document, MathReview (B. D. Agrawal), ZentralBlatt.
- Referenced by:
- ¶ ‣ §10.22(iv), §10.43(iv).
- Encodings:
- BibTeX
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Integrals of three Bessel functions and Legendre functions. II,J. Math. Phys. 26 (4), pp. 645–655.
- External Links:
- ISSN 0022-2488, Document, MathReview (B. D. Agrawal), ZentralBlatt.
- Referenced by:
- ¶ ‣ §10.22(iv), §10.43(iv).
- Encodings:
- BibTeX
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Some integrals involving three modified Bessel functions. I,J. Math. Phys. 27 (3), pp. 682–687.
- External Links:
- ISSN 0022-2488, Document, MathReview, ZentralBlatt.
- Referenced by:
- ¶ ‣ §10.22(iv), §10.43(iv).
- Encodings:
- BibTeX
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Some integrals involving three modified Bessel functions. II,J. Math. Phys. 27 (3), pp. 688–695.
- External Links:
- ISSN 0022-2488, Document, MathReview, ZentralBlatt.
- Referenced by:
- ¶ ‣ §10.22(iv), §10.43(iv).
- Encodings:
- BibTeX
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Applications of the classical umbral calculus,Algebra Universalis 49 (4), pp. 397–434.
- External Links:
- ISSN 0002-5240, Document, MathReview (George E. Andrews), ZentralBlatt.
- Referenced by:
- §24.4(viii).
- Encodings:
- BibTeX
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Riemann surfaces, plane algebraic curves and their period matrices,J. Symbolic Comput. 26 (6), pp. 789–803.
- External Links:
- ISSN 0747-7171, Document, MathReview (Gabino González Díez), ZentralBlatt.
- Referenced by:
- §21.10(ii).
- Encodings:
- BibTeX
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Problem 72-21, Laplace transforms of Airy functions,SIAM Rev. 15 (4), pp. 796–798.
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Evaluation of Legendre functions of argument greater than one,Comput. Phys. Comm. 105 (2-3), pp. 273–283.
- Notes:
- Double-precision Fortran, maximum accuracy 18S
- External Links:
- ISSN 0010-4655, Document, Code, MathReview, ZentralBlatt.
- Referenced by:
- §14.34(ii).
- Encodings:
- BibTeX
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A code to evaluate prolate and oblate spheroidal harmonics,Comput. Phys. Comm. 108 (2-3), pp. 267–278.
- Notes:
- Double-precision Fortran, maximum accuracy 18S
- External Links:
- Document, Code, ZentralBlatt.
- Referenced by:
- §14.34(ii), §14.34(iii).
- Encodings:
- BibTeX
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Evaluation of toroidal harmonics,Comput. Phys. Comm. 124 (1), pp. 104–122.
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DTORH3 2.0: A new version of a computer program for the evaluation of toroidal harmonics,Comput. Phys. Comm. 139 (2), pp. 186–191.
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Computing toroidal functions for wide ranges of the parameters,J. Comput. Phys. 161 (1), pp. 204–217.
- External Links:
- ISSN 0021-9991, Document, MathReview (Adam Marlewski), ZentralBlatt.
- Referenced by:
- §14.14, §14.15(i), §14.26, §14.31(i), §14.32.
- Encodings:
- BibTeX
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On nonoscillating integrals for computing inhomogeneous Airy functions,Math. Comp. 70 (235), pp. 1183–1194.
- External Links:
- Document, MathReview (Richard B. Paris), ZentralBlatt.
- Referenced by:
- ¶ ‣ §3.5(ix), §9.17(iii).
- Encodings:
- BibTeX
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Algorithm 819: AIZ, BIZ: two Fortran 77 routines for the computation of complex Airy functions,ACM Trans. Math. Software 28 (3), pp. 325–336.
- Notes:
- Double-precision Fortran, maximum accuracy 18S.
- External Links:
- ISSN 0098-3500, Document, TOMS module 819 (in GAMS), MathReview Entry, ZentralBlatt.
- Referenced by:
- §9.20(iii).
- Encodings:
- BibTeX
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Algorithm 822: GIZ, HIZ: two Fortran 77 routines for the computation of complex Scorer functions,ACM Trans. Math. Software 28 (4), pp. 436–447.
- Notes:
- Double-precision Fortran, maximum accuracy 18S.
- External Links:
- ISSN 0098-3500, Document, TOMS module 822 (in GAMS), MathReview Entry, ZentralBlatt.
- Referenced by:
- §9.20(vi).
- Encodings:
- BibTeX
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Computing complex Airy functions by numerical quadrature,Numer. Algorithms 30 (1), pp. 11–23.
- External Links:
- ISSN 1017-1398, Document, MathReview (Richard B. Paris), ZentralBlatt.
- Referenced by:
- §9.17(iii).
- Encodings:
- BibTeX
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Evaluation of the modified Bessel function of the third kind of imaginary orders,J. Comput. Phys. 175 (2), pp. 398–411.
- External Links:
- ISSN 0021-9991, Document, MathReview (J. P. Singhal), ZentralBlatt.
- Referenced by:
- §10.74(viii).
- Encodings:
- BibTeX
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Computation of the modified Bessel function of the third kind of imaginary orders: Uniform Airy-type asymptotic expansion,J. Comput. Appl. Math. 153 (1-2), pp. 225–234.
- External Links:
- ISSN 0377-0427, Document, MathReview, ZentralBlatt.
- Referenced by:
- §10.45, §10.74(viii).
- Encodings:
- BibTeX
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Computing special functions by using quadrature rules,Numer. Algorithms 33 (1-4), pp. 265–275.
- Notes:
- International Conference on Numerical Algorithms, Vol. I (Marrakesh, 2001)
- External Links:
- ISSN 1017-1398, Document, MathReview, ZentralBlatt.
- Referenced by:
- ¶ ‣ §3.5(ix).
- Encodings:
- BibTeX
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On the zeros of the Scorer functions,J. Approx. Theory 120 (2), pp. 253–266.
- External Links:
- ISSN 0021-9045, Document, MathReview (Boro Döring), ZentralBlatt.
- Referenced by:
- §9.12(ix), §9.17(v), §9.18(vi).
- Encodings:
- BibTeX
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Algorithm 831: Modified Bessel functions of imaginary order and positive argument,ACM Trans. Math. Software 30 (2), pp. 159–164.
- External Links:
- ISSN 0098-3500, Document, TOMS module 831 (in GAMS), MathReview Entry, ZentralBlatt.
- Referenced by:
- §10.77(vi).
- Encodings:
- BibTeX
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Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments,ACM Trans. Math. Software 30 (2), pp. 145–158.
- External Links:
- ISSN 0098-3500, Document, MathReview, ZentralBlatt.
- Referenced by:
- §10.74(viii).
- Encodings:
- BibTeX
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Integral representations for computing real parabolic cylinder functions,Numer. Math. 98 (1), pp. 105–134.
- External Links:
- ISSN 0029-599X, Document, MathReview Entry, ZentralBlatt.
- Referenced by:
- §12.18.
- Encodings:
- BibTeX
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Computing the real parabolic cylinder functions
, 
,ACM Trans. Math. Software 32 (1), pp. 70–101.- External Links:
- ISSN 0098-3500, Document, MathReview (Syamal K. Sen).
- Referenced by:
- §12.18.
- Encodings:
- BibTeX
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Algorithm 850: Real parabolic cylinder functions, ,ACM Trans. Math. Software 32 (1), pp. 102–112.
- External Links:
- ISSN 0098-3500, Document, MathReview (Syamal K. Sen).
- Referenced by:
- §12.18, §12.21(ii).
- Encodings:
- BibTeX
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The ABC of hyper recursions,J. Comput. Appl. Math. 190 (1-2), pp. 270–286.
- External Links:
- ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt.
- Referenced by:
- §15.19(iv).
- Encodings:
- BibTeX
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Numerical Methods for Special Functions,Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
- External Links:
- ISBN 978-0-898716-34-4, MathReview Entry, ZentralBlatt.
- Referenced by:
- ¶ ‣ §3.10(iii), §3.11(ii), §3.5(v), §3.6(iii), ¶ ‣ §3.8(iii), §3.8(v), Ch.3, Amparo Gil, Javier Segura, Nico M. Temme.
- Encodings:
- BibTeX
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Numerically satisfactory solutions of hypergeometric recursions,Math. Comp. 76 (259), pp. 1449–1468.
- External Links:
- ISSN 0025-5718, FullText, Document, MathReview Entry, ZentralBlatt.
- Referenced by:
- §15.19(iv).
- Encodings:
- BibTeX
-
Computing the zeros and turning points of solutions of second order homogeneous linear ODEs,SIAM J. Numer. Anal. 41 (3), pp. 827–855.
- External Links:
- ISSN 0036-1429, Document, MathReview, ZentralBlatt.
- Referenced by:
- ¶ ‣ §10.74(vi), §3.8(v).
- Encodings:
- BibTeX
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Analysis in homogeneous domains,Uspehi Mat. Nauk 19 (4 (118)), pp. 3–92 (Russian).
- Notes:
- In Russian. English translation: Russian Math. Surveys, 19(1964), no. 4, pp. 1–89
- External Links:
- Document, MathReview (A. Korányi), ZentralBlatt.
- Referenced by:
- §35.3(i).
- Encodings:
- BibTeX
-
A new identity for some six-
symbols,J. Math. Phys. 32 (6), pp. 1430–1432. -
Algorithm 490: The Dilogarithm function of a real argument [S22],Comm. ACM 18 (4), pp. 200–202.
-
A theorem on the numerators of the Bernoulli numbers,Amer. Math. Monthly 97 (2), pp. 136–138.
- External Links:
- ISSN 0002-9890, FullText, MathReview (L. Skula), ZentralBlatt.
- Referenced by:
- §24.10(iv), §24.16(iii).
- Encodings:
- BibTeX
-
Dirichlet convolution of cotangent numbers and relative class number formulas,Monatsh. Math. 110 (3-4), pp. 231–256.
- External Links:
- ISSN 0026-9255, MathReview (Peter Stevenhagen), ZentralBlatt.
- Referenced by:
- §24.16(iii).
- Encodings:
- BibTeX
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Number-Divisor Tables,British Association Mathematical Tables, Vol. VIII, Cambridge University Press, Cambridge, England.
-
Definite integrals of the complete elliptic integral
,J. Res. Nat. Bur. Standards Sect. B 80B (2), pp. 313–323.- External Links:
- MathReview (H. E. Fettis), ZentralBlatt.
- Referenced by:
- §19.13(i).
- Encodings:
- BibTeX
-
A method for evaluating certain Bessel integrals,Z. Angew. Math. Phys. 30 (4), pp. 722–723.
-
Algorithm 745: Computation of the complete and incomplete Fermi-Dirac integral,ACM Trans. Math. Software 21 (3), pp. 221–232.
- Notes:
- Double-precision Fortran, maximum accuracy 20D.
- External Links:
- ISSN 0098-3500, Document, TOMS module 745 (in GAMS), ZentralBlatt.
- Referenced by:
- §25.21(vii).
- Encodings:
- BibTeX
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Combinatorics in Statistical Physics,in Handbook of Combinatorics, Vol. 2,(M. Grötschel and L. Lovász Eds.), pp. 1925–1954.
-
Plancherel-Rotach asymptotics for the Charlier polynomials,Constr. Approx. 14 (2), pp. 151–168.
- External Links:
- ISSN 0176-4276, Document, MathReview (Timothy S. Norfolk), ZentralBlatt.
- Referenced by:
- ¶ ‣ §18.24.
- Encodings:
- BibTeX
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What every computer scientist should know about floating-point arithmetic,ACM Computing Surveys 23 (1), pp. 5–48.
-
Tables of binomial coefficients and Stirling numbers,J. Res. Nat. Bur. Standards Sect. B 80B (1), pp. 99–171.
-
Mathieu functions,Trans. Camb. Philos. Soc. 23, pp. 303–336.
-
Matrix Computations,3rd edition, Johns Hopkins University Press, Baltimore, MD.
- External Links:
- ISBN 0-8018-5413-X; 0-8018-5414-8, MathReview, ZentralBlatt.
- Referenced by:
- ¶ ‣ §3.2(i), §3.2(i), §3.2(ii), §3.2(vii).
- Encodings:
- BibTeX
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Calculation of Gauss quadrature rules,Math. Comp. 23 (106), pp. 221–230.
- Notes:
- Loose microfiche suppl. A1–A10
- External Links:
- FullText, MathReview (F. Stenger), ZentralBlatt.
- Referenced by:
- §3.5(vi).
- Encodings:
- BibTeX
-
Lectures on Integration of the Equations of Motion of a Rigid Body About a Fixed Point,Translated from the Russian by J. Shorr-Kon, Office of Technical Services, U. S. Department of Commerce, Washington, D. C..
- Notes:
- Published for the National Science Foundation by the Israel Program for Scientific Translations, 1960.
- External Links:
- MathReview, ZentralBlatt.
- Referenced by:
- §22.19(iv).
- Encodings:
- BibTeX
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Generalized Fermi-Dirac functions and derivatives: Properties and evaluation,Comput. Phys. Comm. 136 (3), pp. 294–309.
- Notes:
- Double-precision Fortran, maximum accuracy 20D
- External Links:
- Document, Code, ZentralBlatt.
- Referenced by:
- §25.21(vii).
- Encodings:
- BibTeX
-
Table of
,Quart. J. Mech. Appl. Math. 1 (1), pp. 319–326.- External Links:
- Document, MathReview (J. G. van der Corput), ZentralBlatt.
- Referenced by:
- §7.22(ii).
- Encodings:
- BibTeX
-
Recurrence relations for cross-products of Bessel functions,Quart. J. Mech. Appl. Math. 2 (1), pp. 72–74.
- External Links:
- ISSN 0033-5614, Document, MathReview (A. Erdélyi), ZentralBlatt.
- Referenced by:
- §10.6(iii).
- Encodings:
- BibTeX
-
The evaluation of integrals of the form
,Proc. Cambridge Philos. Soc. 45 (2), pp. 241–245. -
New method for constructing wavefunctions for bound states and scattering,J. Chem. Phys. 51, pp. 14–25.
- External Links:
- Document, MathReview (K. J. Le Couteur).
- Referenced by:
- §9.11(iv), §9.17(iii).
- Encodings:
- BibTeX
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Constructing wavefunctions for nonlocal potentials,J. Chem. Phys. 52, pp. 6211–6217.
- External Links:
- Document, MathReview (D. B. Fairlie).
- Referenced by:
- §9.12(vii), §9.17(iii).
- Encodings:
- BibTeX
-
Von Staudt for
![{\mathbf{F}}_{{q}}[{T}]](.././bib/m131.png)
,Duke Math. J. 45 (4), pp. 885–910.- External Links:
- ISSN 0012-7094, Document, MathReview (Neal Koblitz), ZentralBlatt.
- Referenced by:
- §24.16(iii).
- Encodings:
- BibTeX
-
Numerical Analysis of Spectral Methods: Theory and Applications,Society for Industrial and Applied Mathematics, Philadelphia, PA.
- Notes:
- CBMS-NSF Regional Conference Series in Applied Mathematics, No. 26
- External Links:
- MathReview (O. Widlund), ZentralBlatt.
- Referenced by:
- ¶ ‣ §18.38(i).
- Encodings:
- BibTeX
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On the exceptional zeros of cross-products of derivatives of spherical Bessel functions,Z. Angew. Math. Phys. 36 (3), pp. 491–494.
- External Links:
- ISSN 0044-2275, Document, MathReview (B. R. Bhonsle), ZentralBlatt.
- Referenced by:
- §10.58.
- Encodings:
- BibTeX
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Stirling number representation problems,Proc. Amer. Math. Soc. 11 (3), pp. 447–451.
- External Links:
- FullText, MathReview (L. Carlitz), ZentralBlatt.
- Referenced by:
- ¶ ‣ §26.1, ¶ ‣ §26.1.
- Encodings:
- BibTeX
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Explicit formulas for Bernoulli numbers,Amer. Math. Monthly 79, pp. 44–51.
- External Links:
- FullText, MathReview (B. M. Stewart), ZentralBlatt.
- Referenced by:
- §24.15(iii), §24.6.
- Encodings:
- BibTeX
-
Mémoire sur les fonctions hypergéométriques d’ordre supérieur,Ann. Sci. École Norm. Sup. (2) 12, pp. 261–286, 395–430 (French).
-
Sur l’équation différentielle linéaire, qui admet pour intégrale la série hypergéométrique,Ann. Sci. École Norm. Sup. (2) 10, pp. 3–142 (French).
- External Links:
- ISSN 0012-9593, MathReview Entry, ZentralBlatt.
- Referenced by:
- ¶ ‣ §15.8(v), §15.8(v).
- Encodings:
- BibTeX
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Method for evaluation of zeros of Bessel functions,J. Inst. Math. Appl. 11, pp. 57–72.
- External Links:
- ISSN 0020-2932, Document, MathReview (H. E. Fettis), ZentralBlatt.
- Referenced by:
- ¶ ‣ §10.74(vi), ¶ ‣ §3.8(iii).
- Encodings:
- BibTeX
-
Table of Integrals, Series, and Products,6th edition, Academic Press Inc., San Diego, CA.
- Notes:
- Translated from the Russian. Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger. For a review of the fourth edition (1980), with errata list, see Math. Comp. v. 36 (1981), pp. 310–314. For a review of the fifth edition (1994) see Math. Comp. v. 64 (1995), pp. 439–441.
- External Links:
- Errata in the 4th, 5th, and 6th editions, ISBN 0-12-294757-6, Link, MathReview, ZentralBlatt.
- Referenced by:
- §1.14(viii), ¶ ‣ §1.4(iv), §1.8(v), §10.22(vi), §10.23(iv), §10.43(vi), §10.60(iv), §11.7(v), §11.9(iv), ¶ ‣ §12.12, §12.5(iv), §13.10(vi), §13.23(v), §14.18(iv), §15.14, §18.17(ix), §18.18(ix), §19.25(v), §19.29(i), §19.29(ii), §20.10(iii), §22.14(ii), §22.14(iii), §23.14, §24.7(iii), §28.10(iii), §28.28(v), §4.10(iii), §4.11, §4.26(v), §4.27, §4.40(v), §4.41, ¶ ‣ §5.13, §6.14(iii), §7.14(iii), §8.14.
- Encodings:
- BibTeX
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Handbook of Combinatorics. Vols. 1, 2,Elsevier Science B.V., Amsterdam.
- External Links:
- ISBN 0-444-88002-X, MathReview, ZentralBlatt.
- Referenced by:
- §26.19, §26.20, Ch.26.
- Encodings:
- BibTeX
-
Concrete Mathematics: A Foundation for Computer Science,2nd edition, Addison-Wesley Publishing Company, Reading, MA.
- External Links:
- ISBN 0-201-55802-5, MathReview (Volker Strehl), ZentralBlatt.
- Referenced by:
- §24.15(ii), ¶ ‣ §24.17(i), ¶ ‣ §26.1, ¶ ‣ §26.1, §26.14(i), §26.14(ii), §26.14(iii), §26.14(iv), §26.8(iii), §26.8(iv), §26.8(v).
- Encodings:
- BibTeX
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Do integrable mappings have the Painlevé property?,Phys. Rev. Lett. 67 (14), pp. 1825–1828.
- External Links:
- ISSN 0031-9007, Document, MathReview, ZentralBlatt.
- Referenced by:
- ¶ ‣ §32.16.
- Encodings:
- BibTeX
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An application of Airy functions to the Tricomi problem,Math. Nachr. 102 (1), pp. 169–181.
- External Links:
- ISSN 0025-584X, Document, MathReview (John M. S. Rassias), ZentralBlatt.
- Referenced by:
- §9.16.
- Encodings:
- BibTeX
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A Treatise on Bessel Functions and their Applications to Physics,2nd edition, Macmillan and Co., London.
- Notes:
- Table errata: Math. Comp. v. 24 (1970), p. 240, v. 31 (1978), pp. 806 and 1046, and v. 32 (1978), pp. 318. Reprinted by Dover Publications Inc., New York, 1966.
- External Links:
- MathReview, ZentralBlatt.
- Referenced by:
- §10.21(x), §10.73(i), §10.73(i).
- Encodings:
- BibTeX
-
Linear Differential Equations and Group Theory from Riemann to Poincaré,2nd edition, Birkhäuser Boston Inc., Boston, MA.
- External Links:
- ISBN 0-8176-3837-7, MathReview, ZentralBlatt.
- Referenced by:
- §15.17(v).
- Encodings:
- BibTeX
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Automatic reduction of elliptic integrals using Carlson’s relations,Math. Comp. 71 (237), pp. 311–318.
- External Links:
- ISSN 0025-5718, Document, MathReview (David A. Richter), ZentralBlatt.
- Referenced by:
- §19.29(ii).
- Encodings:
- BibTeX
-
Superstring Theory: Introduction, Vol. 1,2nd edition, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.
- External Links:
- ISBN 0-521-35752-7, MathReview, ZentralBlatt.
- Referenced by:
- §20.12(ii), §23.21(iv).
- Encodings:
- BibTeX
-
Superstring Theory: Loop Amplitudes, Anomalies and Phenomenolgy, Vol. 2.,2nd edition, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.
- External Links:
- ISBN 0-521-35753-5, MathReview, ZentralBlatt.
- Referenced by:
- §20.12(ii).
- Encodings:
- BibTeX
-
General form of the quantum-defect theory,Phys. Rev. A 19 (4), pp. 1485–1509.
-
Mathematics for the Analysis of Algorithms,Progress in Computer Science, Vol. 1, Birkhäuser Boston, Boston, MA.
- External Links:
- MathReview (Ernst-Erich Doberkat), ZentralBlatt.
- Referenced by:
- §5.17.
- Encodings:
- BibTeX
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The Applications of Elliptic Functions,MacMillan, London.
- Notes:
- Reprinted by Dover Publications Inc., New York, 1959.
- External Links:
- Link, ZentralBlatt.
- Referenced by:
- §19.30(iii), Ch.19.
- Encodings:
- BibTeX
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The Applications of Elliptic Functions,Dover Publications Inc., New York.
- Notes:
- Reprint of Macmillan, London edition, 1892
- External Links:
- MathReview, ZentralBlatt.
- Referenced by:
- §22.18(iii), §22.19(iv), §22.8(iii).
- Encodings:
- BibTeX
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Quantum Electrodynamics of Strong Fields: With an Introduction into Modern Relativistic Quantum Mechanics,Texts and Monographs in Physics, Springer.
-
A monotonicity property of the power function of multivariate tests,Indag. Math. (N.S.) 11 (2), pp. 209–218.
- External Links:
- ISSN 0019-3577, Document, MathReview (Sumitra Purkayastha), ZentralBlatt.
- Referenced by:
- §35.9.
- Encodings:
- BibTeX
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Special classes of solutions of Painlevé equations,Differ. Uravn. 18 (3), pp. 419–429 (Russian).
- Notes:
- In Russian. English translation: Differential Equations 18(3), pp. 317–326.
- External Links:
- ISSN 0374-0641, MathReview, ZentralBlatt.
- Referenced by:
- §32.10(iv), §32.10(v), §32.8(iii), §32.8(v), §32.9(ii).
- Encodings:
- BibTeX
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Theory of Painlevé’s equations,Differ. Uravn. 11 (11), pp. 373–376 (Russian).
- Notes:
- In Russian. English translation: Differential Equations 11(11), pp. 285–287
- External Links:
- MathReview (Z. Nehari), ZentralBlatt.
- Referenced by:
- §32.7(iii), §32.7(vi).
- Encodings:
- BibTeX
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The solutions of Painlevé’s fifth equation,Differ. Uravn. 12 (4), pp. 740–742 (Russian).
- Notes:
- In Russian. English translation: Differential Equations 12(4), pp. 519–521 (1977)
- External Links:
- MathReview (Z. Nehari), ZentralBlatt.
- Referenced by:
- §32.7(v).
- Encodings:
- BibTeX
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One-parameter systems of solutions of Painlevé equations,Differ. Uravn. 14 (12), pp. 2131–2135 (Russian).
- Notes:
- In Russian. English translation: Differential Equations 14(12), pp. 1510–1513 (1979)
- External Links:
- ISSN 0374-0641, MathReview (M. Tvrdý), ZentralBlatt.
- Referenced by:
- §32.10(i), §32.10(ii), §32.10(iii), §32.7(iv).
- Encodings:
- BibTeX
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Theory of the fourth Painlevé equation,Differ. Uravn. 23 (5), pp. 760–768, 914 (Russian).
- Notes:
- In Russian. English translation: Differential Equations 23(5), pp. 506–513
- External Links:
- ISSN 0374-0641, MathReview (C. S. Coleman), ZentralBlatt.
- Referenced by:
- §32.10(iv), §32.7(iv), §32.8(iv).
- Encodings:
- BibTeX
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Painlevé Differential Equations in the Complex Plane,Studies in Mathematics, Vol. 28, Walter de Gruyter & Co., Berlin-New York.
- External Links:
- ISBN 3-11-017379-4, MathReview, ZentralBlatt.
- Referenced by:
- §32.10(i), §32.10(iii), §32.10(iv), §32.10(v), §32.10(vi), §32.2(iv), §32.7(iii), §32.7(iv), §32.7(v), §32.7(vi), §32.7(vii), §32.8(ii), §32.8(iii), §32.8(iv), §32.8(v), §32.9(i), §32.9(ii), §32.9(iii).
- Encodings:
- BibTeX
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Bessel functions and representation theory. I,J. Functional Analysis 22 (2), pp. 73–105.
- External Links:
- Document, MathReview (E. A. Thieleker), ZentralBlatt.
- Referenced by:
- §35.5(i).
- Encodings:
- BibTeX
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Special functions of matrix argument. I. Algebraic induction, zonal polynomials, and hypergeometric functions,Trans. Amer. Math. Soc. 301 (2), pp. 781–811.
- External Links:
- ISSN 0002-9947, FullText, MathReview (Wayne J. Holman, III), ZentralBlatt.
- Referenced by:
- ¶ ‣ §35.8(i), §35.8(ii), §35.8(iv), Ch.35.
- Encodings:
- BibTeX
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Hypergeometric functions on complex matrix space,Bull. Amer. Math. Soc. (N.S.) 24 (2), pp. 349–355.
- External Links:
- ISSN 0273-0979, Document, MathReview, ZentralBlatt.
- Referenced by:
- §35.7(iii), ¶ ‣ §35.8(i), §35.8(ii), §35.8(iii), §35.8(iv).
- Encodings:
- BibTeX
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Bessel Polynomials,Lecture Notes in Mathematics, Vol. 698, Springer, Berlin-New York.
- External Links:
- ISBN 3-540-09104-1, MathReview (Mourad E. H. Ismail), ZentralBlatt.
- Referenced by:
- §10.49(ii).
- Encodings:
- BibTeX
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Representations of Integers as Sums of Squares,Springer-Verlag, New York.
- External Links:
- ISBN 0-387-96126-7, MathReview (Harvey Cohn), ZentralBlatt.
- Referenced by:
- §27.13(iv).
- Encodings:
- BibTeX
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Inductance Calculations,Van Nostrand, New York.
- Notes:
- Reprinted by Dover, New York, 1962 and 2004
- External Links:
- ZentralBlatt.
- Referenced by:
- §19.34.
- Encodings:
- BibTeX
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Integraltafel. Erster Teil. Unbestimmte Integrale,Springer-Verlag, Vienna.
- Notes:
- Reprintings with corrections appeared in 1961 and 1965
- External Links:
- MathReview (R. P. Boas, Jr.), ZentralBlatt.
- Referenced by:
- ¶ ‣ §1.4(iv), §23.14, §4.10(iii), §4.26(v), §4.40(v).
- Encodings:
- BibTeX
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Integraltafel. Zweiter Teil. Bestimmte Integrale,Springer-Verlag, Vienna and Innsbruck.
- Notes:
- Reprintings with corrections appeared in 1958 and 1961
- External Links:
- MathReview (J. V. Wehausen), ZentralBlatt.
- Referenced by:
- ¶ ‣ §1.4(iv), §10.22(vi), §10.32(iv), §10.43(vi), §10.9(iv), §18.17(ix), §4.10(iii), §4.26(v), §4.40(v).
- Encodings:
- BibTeX
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GNU Scientific LibraryThe GNU Project.
- Notes:
- The GNU Scientific Library is a large general purpose numerical software library with broad coverage of elementary and special functions. Implementation is in double precision.
- External Links:
- Home Page.
- Referenced by:
- § ‣ § Software Cross Index.
- Encodings:
- BibTeX
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Algorithm 300: Coulomb wave functions,Comm. ACM 10 (4), pp. 244–245.
- Notes:
- For remarks see same journal 12(1969), p. 692 and 16(1973), pp. 308-309 and for certification see same journal 12(1969), pp. 279-280.
- External Links:
- ISSN 0001-0782, Document.
- Referenced by:
- §33.26(ii).
- Encodings:
- BibTeX
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Spectral Methods and Their Applications,World Scientific Publishing Co. Inc., River Edge, NJ-Singapore.
- External Links:
- ISBN 981-02-3333-7, MathReview (K. Moszyński), ZentralBlatt.
- Referenced by:
- ¶ ‣ §18.38(i).
- Encodings:
- BibTeX
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On Mill’s ratio,Proc. Cambridge Philos. Soc. 67, pp. 363–364.
-
Riccati equations and convolution formulae for functions of Rayleigh type,J. Phys. A 33 (7), pp. 1363–1368.
- External Links:
- ISSN 0305-4470, Document, MathReview, ZentralBlatt.
- Referenced by:
- §10.21(xiii).
- Encodings:
- BibTeX
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Tables of Partitions,Royal Society Math. Tables, Vol. 4, Cambridge University Press.
-
A table of partitions,Proc. London Math. Soc. (2) 39, pp. 142–149.
-
A table of partitions,Proc. London Math. Soc. (2) 42, pp. 546–549.
-
Multilateral summation theorems for ordinary and basic hypergeometric series in
,SIAM J. Math. Anal. 18 (6), pp. 1576–1596.- External Links:
- ISSN 0036-1410, Document, MathReview, ZentralBlatt.
- Referenced by:
- §17.15.
- Encodings:
- BibTeX
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Asymptotische Entwicklungen für unvollständige Gammafunktionen,Forum Math. 3 (2), pp. 105–141 (German).
- Notes:
- Translated title: Asymptotic expansions for incomplete gamma functions.
- External Links:
- ISSN 0933-7741, MathReview (T. Erber), ZentralBlatt.
- Referenced by:
- §8.16.
- Encodings:
- BibTeX
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Mathieu functions, a visual approach,Amer. J. Phys. 71 (3), pp. 233–242.
-
Staircase polygons, elliptic integrals, Heun functions, and lattice Green functions,Phys. Rev. E 47 (4), pp. R2233–R2236.
-
The solution of Cauchy’s problem for two totally hyperbolic linear differential equations by means of Riesz integrals,Ann. of Math. (2) 48 (4), pp. 785–826.
- External Links:
- FullText, MathReview (E. T. Copson), ZentralBlatt.
- Referenced by:
- §35.2, §35.3(ii).
- Encodings:
- BibTeX