linearization%20formulas

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1: Bibliography

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Exact linearization of a Painlevé transcendent. Phys. Rev. Lett. 38 (20), pp. 1103–1106.

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External Links:

Document, MathReview (Mark Adler)

Referenced by:

§32.11(ii), §32.13(i), §32.13(ii), §32.13(iii), §32.5.

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On the degrees of irreducible factors of higher order Bernoulli polynomials. Acta Arith. 62 (4), pp. 329–342.

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External Links:

ISSN 0065-1036, Pdf, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.12(iii).

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Repeated integrals and derivatives of $K$ Bessel functions. SIAM J. Math. Anal. 20 (1), pp. 169–175.

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ISSN 0036-1410, Document, MathReview (A. Haimovici), ZentralBlatt

Referenced by:

§10.43(iii).

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Bernoulli’s power-sum formulas revisited. Math. Gaz. 90 (518), pp. 276–279.

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Referenced by:

§24.4(iii).

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Linear algebra done right. Third edition, Undergraduate Texts in Mathematics, Springer, Cham.

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External Links:

ISBN 978-3-319-11079-0; 978-3-319-11080-6, Document, Link, MathReview Entry

Referenced by:

§1.2(v), §1.2(vi), §1.3(iv).

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2: Bibliography K

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Quasi-linear Stokes phenomenon for the Painlevé first equation. J. Phys. A 37 (46), pp. 11149–11167.

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External Links:

ISSN 0305-4470, Document, MathReview (W. Balser), ZentralBlatt

Referenced by:

§32.12(i).

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Linear convergence and the bisection algorithm. Amer. Math. Monthly 93 (1), pp. 48–51.

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External Links:

ISSN 0002-9890, FullText, MathReview (J. G. Herriot), ZentralBlatt

Referenced by:

§3.8(iii).

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On formulas involving both the Bernoulli and Fibonacci numbers. Scripta Math. 23, pp. 27–35.

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External Links:

MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§24.15(iv).

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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.

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ISSN 0266-5611, Document, MathReview (Shun Shimomura), ZentralBlatt

Referenced by:

§32.11(iv).

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An algorithm for solving second order linear homogeneous differential equations. J. Symbolic Comput. 2 (1), pp. 3–43.

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ISSN 0747-7171, MathReview, ZentralBlatt

Referenced by:

§31.14(ii).

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3: Bibliography G

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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.

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External Links:

FullText, MathReview (E. T. Copson), ZentralBlatt

Referenced by:

§35.2, §35.3(ii).

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The Computation of Special Functions by Linear Difference Equations. In Advances in Difference Equations (Veszprém, 1995), S. Elaydi, I. Győri, and G. Ladas (Eds.), pp. 213–243.

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External Links:

ISBN 90-5699-521-9, MathReview, ZentralBlatt

Referenced by:

§3.6(iii), §3.6(vii).

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Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

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Notes:

Includes Fortran program claiming 12S accuracy

External Links:

ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt

Referenced by:

3rd item, §10.77(ix).

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Linear Differential Equations and Group Theory from Riemann to Poincaré. 2nd edition, Birkhäuser Boston Inc., Boston, MA.

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External Links:

ISBN 0-8176-3837-7, MathReview, ZentralBlatt

Referenced by:

§15.17(v).

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Kinetic theory of linear shear flow. Phys. Fluids 1 (3), pp. 215–224.

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Referenced by:

§18.39(iii).

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4: Bibliography F

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Notes:

The “Freely Distributable LIBM” package provides implementations of standard elementary functions plus a few higher functions, e.g. gamma. Double precision, maximum accuracy 20S. Developed by Sun Microsystems.

External Links:

GAMS (package FDLIBM)

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index.

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Sur certaines sommes des intégral-cosinus. Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).

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External Links:

MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§6.15.

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The Edmonds asymptotic formulas for the $3j$ and $6j$ symbols. J. Math. Phys. 39 (7), pp. 3906–3915.

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External Links:

ISSN 0022-2488, Document, MathReview (A. J. Coleman), ZentralBlatt

Referenced by:

§34.8.

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On weighted polynomial approximation on the whole real axis. Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.

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ISSN 0001-5954, Document, Link, MathReview (A. K. Varma)

Referenced by:

§18.32.

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Über lineare homogene Differentialgleichungen zweiter Ordnung mit drei im Endlichen gelegenen wesentlich singulären Stellen. Math. Ann. 63 (3), pp. 301–321.

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External Links:

ISSN 0025-5831, Document, ZentralBlatt

Referenced by:

§32.2(iv).

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5: Bibliography W

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Asymptotic expansions for second-order linear difference equations with a turning point. Numer. Math. 94 (1), pp. 147–194.

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ISSN 0029-599X, Document, MathReview (Sergey M. Zagorodnyuk), ZentralBlatt

Referenced by:

§2.9(iii).

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Linear difference equations with transition points. Math. Comp. 74 (250), pp. 629–653.

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External Links:

ISSN 0025-5718, Document, MathReview (B. G. Pachpatte), ZentralBlatt

Referenced by:

§2.9(iii).

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Linear Turning Point Theory. Applied Mathematical Sciences No. 54, Springer-Verlag, New York.

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External Links:

ISBN 0-387-96046-5, MathReview (Anthony Leung), ZentralBlatt

Referenced by:

Ch.9.

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Linear and Nonlinear Waves. John Wiley & Sons, New York.

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Notes:

Reprinted in 1999.

External Links:

ISBN 0471359424, MathReview, ZentralBlatt

Referenced by:

§9.16.

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Asymptotics of linear recurrences. Anal. Appl. (Singap.) 12 (4), pp. 463–484.

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External Links:

ISSN 0219-5305, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§2.9(iii), §2.9(iii).

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6: Bibliography S

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Non-linear transformations of divergent and slowly convergent sequences. J. Math. Phys. 34, pp. 1–42.

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External Links:

MathReview (J. Kuntzmann), ZentralBlatt

Referenced by:

§17.18.

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Introduction to the Theory of Linear Spaces. Martino, Mansfield Center, CT.

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Notes:

republication of 1961 first edition, Prentice-Hall,New Jersey

External Links:

ISBN 978-1-61427-457-5, MathReview Entry

Referenced by:

§1.18(i), §1.2(vi), §1.3(iv).

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Non-linear integral equations for Heun functions. Proc. Edinburgh Math. Soc. (2) 16, pp. 281–289.

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External Links:

Document, MathReview (J. D. DePree), ZentralBlatt

Referenced by:

§31.10(ii).

Encodings:

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Liouville-Green approximations for a class of linear oscillatory difference equations of the second order. J. Comput. Appl. Math. 41 (1-2), pp. 105–116.

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External Links:

ISSN 0377-0427, Document, MathReview (Wan Biao Ma), ZentralBlatt

Referenced by:

§2.9(iii).

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The linear differential equation whose solutions are the products of solutions of two given differential equations. J. Math. Anal. Appl. 98 (1), pp. 130–147.

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ISSN 0022-247X, Document, FullText, MathReview (Wolfgang Bühring), ZentralBlatt

Referenced by:

§1.13(v).

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7: Bibliography R

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A non-negative representation of the linearization coefficients of the product of Jacobi polynomials. Canad. J. Math. 33 (4), pp. 915–928.

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ISSN 0008-414X, Document, Link, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.18(v).

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On the definition and properties of generalized $6$-$j$ symbols. J. Math. Phys. 20 (12), pp. 2398–2415.

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ISSN 0022-2488, Document, MathReview (S. Saran), ZentralBlatt

Referenced by:

§16.4(iii), §16.4(iii).

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Fourier analysis and signal processing by use of the Möbius inversion formula. IEEE Trans. Acoustics, Speech, Signal Processing 38, pp. 458–470.

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External Links:

ZentralBlatt

Referenced by:

§27.17.

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General Computation Methods of Chebyshev Approximation. The Problems with Linear Real Parameters. Publishing House of the Academy of Science of the Ukrainian SSR, Kiev.

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Notes:

English translation, AEC-TR-4491, United States Atomic Energy Commission

External Links:

MathReview (A. S. Householder)

Referenced by:

§3.11(iii).

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Another proof of the triple sum formula for Wigner $9j$-symbols. J. Math. Phys. 40 (12), pp. 6689–6691.

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External Links:

ISSN 0022-2488, Document, MathReview (Michael Wüstner), ZentralBlatt

Referenced by:

§34.6.

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8: Bibliography N

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On simplified asymptotic formulas for a class of Mathieu functions. SIAM J. Math. Anal. 15 (6), pp. 1205–1213.

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ISSN 0036-1410, Document, MathReview (Harold Exton), ZentralBlatt

Referenced by:

§28.26(ii).

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On an integral transform involving a class of Mathieu functions. SIAM J. Math. Anal. 20 (6), pp. 1500–1513.

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External Links:

ISSN 0036-1410, Document, MathReview (K. C. Gupta), ZentralBlatt

Referenced by:

§28.26(ii).

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Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.

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External Links:

FullText, MathReview (I. A. Stegun), ZentralBlatt

Referenced by:

§19.37(iv).

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Uniform Asymptotic Approximations of Solutions of Second-order Linear Differential Equations, with a Coalescing Simple Turning Point and Simple Pole. Ph.D. Thesis, University of Maryland, College Park, MD.

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Referenced by:

§2.8(vi).

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A table of integrals of the error functions. J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.

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Notes:

See for additions and corrections same journal, Sect. B 75, 149–163 (1975)

External Links:

MathReview, ZentralBlatt

Referenced by:

§7.14(iii), §7.21, §7.7(iii).

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9: Bibliography D

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Complex zeros of linear combinations of spherical Bessel functions and their derivatives. SIAM J. Math. Anal. 4 (1), pp. 128–133.

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ISSN 1095-7154, Document, MathReview (C. J. Bouwkamp), ZentralBlatt

Referenced by:

§10.58.

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Computing spectra of linear operators using the Floquet-Fourier-Hill method. J. Comput. Phys. 219 (1), pp. 296–321.

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External Links:

ISSN 0021-9991, MathReview, ZentralBlatt

Referenced by:

§22.11.

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A simple sum formula for Clebsch-Gordan coefficients. Lett. Math. Phys. 5 (3), pp. 207–211.

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External Links:

ISSN 0377-9017, Document, MathReview, ZentralBlatt

Referenced by:

§14.17(iv).

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Convergent expansions for solutions of linear ordinary differential equations having a simple turning point, with an application to Bessel functions. Stud. Appl. Math. 107 (3), pp. 293–323.

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External Links:

ISSN 0022-2526, Document, MathReview, ZentralBlatt

Referenced by:

§10.20(ii), §2.8(i).

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Olver’s error bound methods applied to linear ordinary differential equations having a simple turning point. Anal. Appl. (Singap.) 12 (4), pp. 385–402.

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External Links:

ISSN 0219-5305, Document, Link, MathReview (Thomas Mbah Acho), ZentralBlatt

Referenced by:

5th item, §14.32.

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10: Bibliography B

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Transcendental Functions Satisfying Nonhomogeneous Linear Differential Equations. The Macmillan Co., New York.

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External Links:

MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§11.4(i), §11.4(v), §11.5(ii), §11.5(i), §11.5(ii), §11.5(iii), §11.7(ii), §11.7(iii), §11.7(v), §11.9(i), §11.9(iv), §11.9(iv), Ch.11, §14.29.

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Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.

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External Links:

Document

Referenced by:

§33.22(iv).

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Mathieu functions of general order: Connection formulae, base functions and asymptotic formulae. I–V. Philos. Trans. Roy. Soc. London Ser. A 301, pp. 75–162.

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External Links:

ISSN 0080-4614, FullText, MathReview (J. Meixner), ZentralBlatt

Referenced by:

§28.8(iv).

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An Introduction to Linear Difference Equations. Dover Publications Inc., New York.

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Notes:

Unaltered republication of the original 1927 Harvard University edition.

External Links:

MathReview, ZentralBlatt

Referenced by:

§8.1, Notations P, Notations Q.

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Error estimates for the solution of linear systems. SIAM J. Sci. Comput. 21 (2), pp. 764–781.

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External Links:

ISSN 1095-7197, Document, MathReview (Dimitrios Noutsos), ZentralBlatt

Referenced by:

§3.2(iii).

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