DLMF: Untitled Document

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K. L. Sala (1989) Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean. SIAM J. Math. Anal. 20 (6), pp. 1514–1528.

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External Links:: ISSN 0036-1410, Document, MathReview (J. M. H. Peters), ZentralBlatt
Referenced by:: §22.19(i), §22.20(vi).
Encodings:: BibTeX

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L. Z. Salchev and V. B. Popov (1976) A property of the zeros of cross-product Bessel functions of different orders. Z. Angew. Math. Mech. 56 (2), pp. 120–121.

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External Links:: Document, MathReview (S. Saran), ZentralBlatt
Referenced by:: §10.21(x).
Encodings:: BibTeX

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A. Sharples (1967) Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.

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External Links:: Document, MathReview (F. W. J. Olver), ZentralBlatt
Referenced by:: §28.8(iv).
Encodings:: BibTeX

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J. R. Stembridge (1995) A Maple package for symmetric functions. J. Symbolic Comput. 20 (5-6), pp. 755–768.

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Notes:: For software see John Stembridge’s home page. The SF package contains Maple software for zonal, Jack, and Macdonald polynomials.
External Links:: Home Page, ISSN 0747-7171, Document, MathReview, ZentralBlatt
Referenced by:: 3rd item.
Encodings:: BibTeX

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F. Stenger (1993) Numerical Methods Based on Sinc and Analytic Functions. Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.

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Notes:: Sinc-Pack, a set of 480 Matlab programs with a 470-page tutorial, is available for purchase from SINC, LLC by contacting Frank Stenger.
External Links:: ISBN 0-387-94008-1, MathReview (B. Boyanov), ZentralBlatt
Referenced by:: §3.3(vi), §3.4(i), §3.5(i).
Encodings:: BibTeX

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§11.14(ii) Struve Functions

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Abramowitz and Stegun (1964, Chapter 12) tabulates $\mathbf{H}_{n}\left(x\right)$ , $\mathbf{H}_{n}\left(x\right)-Y_{n}\left(x\right)$ , and $I_{n}\left(x\right)-\mathbf{L}_{n}\left(x\right)$ for $n=0,1$ and $x=0(.1)5$ , $x^{-1}=0(.01)0.2$ to 6D or 7D.

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Zhang and Jin (1996) tabulates $\mathbf{H}_{n}\left(x\right)$ and $\mathbf{L}_{n}\left(x\right)$ for $n=-4(1)3$ and $x=0(1)20$ to 8D or 7S.

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§11.14(iv) Anger–Weber Functions

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§11.14(v) Incomplete Functions

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P. L. Kapitsa (1951b) The computation of the sums of negative even powers of roots of Bessel functions. Doklady Akad. Nauk SSSR (N.S.) 77, pp. 561–564.

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External Links:: MathReview (A. Erdélyi), ZentralBlatt
Referenced by:: §10.21(xiii).
Encodings:: BibTeX

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R. B. Kearfott, M. Dawande, K. Du, and C. Hu (1994) Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.

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External Links:: ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt
Referenced by:: 1st item.
Encodings:: BibTeX

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M. K. Kerimov and S. L. Skorokhodov (1984a) Calculation of modified Bessel functions in a complex domain. Zh. Vychisl. Mat. i Mat. Fiz. 24 (5), pp. 650–664.

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Notes:: English translation in U.S.S.R. Computational Math. and Math. Phys. 24(3), pp. 15–24
External Links:: ISSN 0044-4669, Document, MathReview (Walter Gautschi), ZentralBlatt
Referenced by:: §10.42, §10.74(iv).
Encodings:: BibTeX

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M. K. Kerimov (1980) Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

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External Links:: Document, MathReview (Matti Jutila), ZentralBlatt
Referenced by:: §25.18(i).
Encodings:: BibTeX

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B. G. Korenev (2002) Bessel Functions and their Applications. Analytical Methods and Special Functions, Vol. 8, Taylor & Francis Ltd., London-New York.

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Notes:: Translated from the Russian by E. V. Pankratiev
External Links:: ISBN 0-415-28130-X, MathReview (L. Debnath), ZentralBlatt
Referenced by:: §10.73(i), §10.73(i), §10.73(i).
Encodings:: BibTeX

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Yu. L. Ratis and P. Fernández de Córdoba (1993) A code to calculate (high order) Bessel functions based on the continued fractions method. Comput. Phys. Comm. 76 (3), pp. 381–388.

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Notes:: Double-precision Fortran, maximum accuracy 18D.
External Links:: ISSN 0010-4655, Document, Code, MathReview, ZentralBlatt
Referenced by:: 6th item.
Encodings:: BibTeX

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J. T. Ratnanather, J. H. Kim, S. Zhang, A. M. J. Davis, and S. K. Lucas (2014) Algorithm 935: IIPBF, a MATLAB toolbox for infinite integral of products of two Bessel functions. ACM Trans. Math. Softw. 40 (2), pp. 14:1–14:12.

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External Links:: ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt
Referenced by:: §10.74(vii), §10.74(vii), 7th item, §10.77(ix).
Encodings:: BibTeX

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F. E. Relton (1965) Applied Bessel Functions. Dover Publications Inc., New York.

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Notes:: Reprint of original Blackie & Son Limited, London, 1946.
External Links:: MathReview, ZentralBlatt
Referenced by:: §10.73(iii).
Encodings:: BibTeX

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G. F. Remenets (1973) Computation of Hankel (Bessel) functions of complex index and argument by numerical integration of a Schläfli contour integral. Ž. Vyčisl. Mat. i Mat. Fiz. 13, pp. 1415–1424, 1636.

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Notes:: English translation in U.S.S.R. Computational Math. and Math. Phys. 13(6), pp. 58–67
External Links:: ISSN 0044-4669, Document, MathReview (H. Zegeling), ZentralBlatt
Referenced by:: §10.74(iii).
Encodings:: BibTeX

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M. D. Rogers (2005) Partial fractions expansions and identities for products of Bessel functions. J. Math. Phys. 46 (4), pp. 043509–1–043509–18.

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External Links:: ISSN 0022-2488, Document, MathReview (Wolfgang zu Castell), ZentralBlatt
Referenced by:: §10.23(ii).
Encodings:: BibTeX

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§30.9(i) Prolate Spheroidal Wave Functions

… ►For uniform asymptotic expansions in terms of Airy or Bessel functions for real values of the parameters, complex values of the variable, and with explicit error bounds see Dunster (1986). … ►

§30.9(ii) Oblate Spheroidal Wave Functions

… ►For uniform asymptotic expansions in terms of elementary, Airy, or Bessel functions for real values of the parameters, complex values of the variable, and with explicit error bounds see Dunster (1992, 1995). … ►

§30.9(iii) Other Approximations and Expansions

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§11.6(i) Large $|z|$ , Fixed $\nu$

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§11.6(ii) Large $|\nu|$ , Fixed $z$

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c_{3}(\lambda)=20\lambda^{-6}-4\lambda^{-4},

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§6.20(i) Approximations in Terms of Elementary Functions

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Cody and Thacher (1968) provides minimax rational approximations for $E_{1}\left(x\right)$ , with accuracies up to 20S.

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Cody and Thacher (1969) provides minimax rational approximations for $\operatorname{Ei}\left(x\right)$ , with accuracies up to 20S.

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MacLeod (1996b) provides rational approximations for the sine and cosine integrals and for the auxiliary functions $\mathrm{f}$ and $\mathrm{g}$ , with accuracies up to 20S.

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Luke (1969b, pp. 41–42) gives Chebyshev expansions of $\operatorname{Ein}\left(ax\right)$ , $\operatorname{Si}\left(ax\right)$ , and $\operatorname{Cin}\left(ax\right)$ for $-1\leq x\leq 1$ , $a\in\mathbb{C}$ . The coefficients are given in terms of series of Bessel functions.

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D. Naylor (1989) 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).
Encodings:: BibTeX

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G. Nemes (2017b) Error Bounds for the Large-Argument Asymptotic Expansions of the Hankel and Bessel Functions. Acta Appl. Math. 150, pp. 141–177.

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External Links:: ISSN 0167-8019, Document, MathReview Entry, ZentralBlatt
Referenced by:: (9.7.16), (9.7.17), §9.7(iii), §9.7(iv).
Encodings:: BibTeX

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E. Neuman (2004) Inequalities involving Bessel functions of the first kind. JIPAM. J. Inequal. Pure Appl. Math. 5 (4), pp. Article 94, 4 pp. (electronic).

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External Links:: ISSN 1443-5756, FullText, MathReview, ZentralBlatt
Referenced by:: §10.14.
Encodings:: BibTeX

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J. N. Newman (1984) Approximations for the Bessel and Struve functions. Math. Comp. 43 (168), pp. 551–556.

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External Links:: ISSN 0025-5718, FullText, MathReview (S. Conde), ZentralBlatt
Referenced by:: 1st item.
Encodings:: BibTeX

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E. W. Ng and M. Geller (1969) 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).
Encodings:: BibTeX

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J. B. Campbell (1980) On Temme’s algorithm for the modified Bessel function of the third kind. ACM Trans. Math. Software 6 (4), pp. 581–586.

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External Links:: ISSN 0098-3500, Document, MathReview, ZentralBlatt
Referenced by:: §10.74(iv).
Encodings:: BibTeX

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R. Cicchetti and A. Faraone (2004) Incomplete Hankel and modified Bessel functions: A class of special functions for electromagnetics. IEEE Trans. Antennas and Propagation 52 (12), pp. 3373–3389.

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External Links:: ISSN 0018-926X, Document, MathReview (T. Erber), ZentralBlatt
Referenced by:: §10.46.
Encodings:: BibTeX

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J. A. Cochran (1963) Further formulas for calculating approximate values of the zeros of certain combinations of Bessel functions. IEEE Trans. Microwave Theory Tech. 11 (6), pp. 546–547.

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External Links:: ISSN 0018-9480, FullText
Referenced by:: §10.21(x).
Encodings:: BibTeX

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J. A. Cochran (1966a) The analyticity of cross-product Bessel function zeros. Proc. Cambridge Philos. Soc. 62, pp. 215–226.

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External Links:: MathReview (R. G. Langebartel), ZentralBlatt
Referenced by:: §10.21(x).
Encodings:: BibTeX

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M. Colman, A. Cuyt, and J. Van Deun (2011) Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

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External Links:: ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt
Referenced by:: §13.29(v), §15.19(v).
Encodings:: BibTeX

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A. Laforgia (1986) Inequalities for Bessel functions. J. Comput. Appl. Math. 15 (1), pp. 75–81.

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External Links:: ISSN 0377-0427, Document, MathReview (B. D. Agrawal), ZentralBlatt
Referenced by:: §10.14.
Encodings:: BibTeX

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A. Laforgia (1991) Bounds for modified Bessel functions. J. Comput. Appl. Math. 34 (3), pp. 263–267.

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External Links:: ISSN 0377-0427, Document, MathReview (N. Hayek Calil), ZentralBlatt
Referenced by:: §10.37.
Encodings:: BibTeX

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L. J. Landau (2000) Bessel functions: Monotonicity and bounds. J. London Math. Soc. (2) 61 (1), pp. 197–215.

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External Links:: ISSN 0024-6107, Document, MathReview (M. E. Muldoon), ZentralBlatt
Referenced by:: §10.14, §10.15.
Encodings:: BibTeX

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P. W. Lawrence, R. M. Corless, and D. J. Jeffrey (2012) Algorithm 917: complex double-precision evaluation of the Wright

\omega

function. ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.

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External Links:: ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt
Referenced by:: §4.13, 2nd item, §4.48(iv).
Encodings:: BibTeX

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S. Lewanowicz (1991) Evaluation of Bessel function integrals with algebraic singularities. J. Comput. Appl. Math. 37 (1-3), pp. 101–112.

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External Links:: ISSN 0377-0427, Document, MathReview, ZentralBlatt
Referenced by:: §10.74(vii).
Encodings:: BibTeX

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as%20Bessel%20functions

11—20 of 26 matching pages

11: Bibliography S

12: 11.14 Tables

§11.14(ii) Struve Functions

§11.14(iv) Anger–Weber Functions

§11.14(v) Incomplete Functions

13: Bibliography K

14: Bibliography R

15: 30.9 Asymptotic Approximations and Expansions

§30.9(i) Prolate Spheroidal Wave Functions

§30.9(ii) Oblate Spheroidal Wave Functions

§30.9(iii) Other Approximations and Expansions

16: 11.6 Asymptotic Expansions

§11.6(i) Large $|z|$ , Fixed $\nu$

§11.6(ii) Large $|\nu|$ , Fixed $z$

17: 6.20 Approximations

§6.20(i) Approximations in Terms of Elementary Functions

18: Bibliography N

19: Bibliography C

20: Bibliography L

as%20Bessel%20functions

11—20 of 26 matching pages

11: Bibliography S

12: 11.14 Tables

§11.14(ii) Struve Functions

§11.14(iv) Anger–Weber Functions

§11.14(v) Incomplete Functions

13: Bibliography K

14: Bibliography R

15: 30.9 Asymptotic Approximations and Expansions

§30.9(i) Prolate Spheroidal Wave Functions

§30.9(ii) Oblate Spheroidal Wave Functions

§30.9(iii) Other Approximations and Expansions

16: 11.6 Asymptotic Expansions

§11.6(i) Large | z | , Fixed ν

§11.6(ii) Large | ν | , Fixed z

17: 6.20 Approximations

§6.20(i) Approximations in Terms of Elementary Functions

18: Bibliography N

19: Bibliography C

20: Bibliography L

§11.6(i) Large $|z|$ , Fixed $\nu$

§11.6(ii) Large $|\nu|$ , Fixed $z$