as%20Bessel%20functions
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21—26 of 26 matching pages
21: Bibliography I
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The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of and of Bessel functions
of any real order
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Linear Algebra Appl. 194, pp. 35–70.
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Computing zeros and orders of Bessel functions.
J. Comput. Appl. Math. 38 (1-3), pp. 169–184.
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Computation of integrals over the half-line involving products of Bessel functions, with application to microwave transmission lines.
Z. Angew. Math. Mech. 75 (12), pp. 917–926.
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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Bounds for the small real and purely imaginary zeros of Bessel and related functions.
Methods Appl. Anal. 2 (1), pp. 1–21.
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22: Bibliography O
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Complete elliptic integrals resulting from infinite integrals of Bessel functions.
J. Res. Nat. Bur. Standards Sect. B 78B (3), pp. 113–135.
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Complete elliptic integrals resulting from infinite integrals of Bessel functions. II.
J. Res. Nat. Bur. Standards Sect. B 79B (3-4), pp. 137–170.
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Asymptotic expansions for -gamma, -exponential, and -Bessel functions.
J. Math. Anal. Appl. 186 (3), pp. 896–913.
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A new method for the evaluation of zeros of Bessel functions and of other solutions of second-order differential equations.
Proc. Cambridge Philos. Soc. 46 (4), pp. 570–580.
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Some new asymptotic expansions for Bessel functions of large orders.
Proc. Cambridge Philos. Soc. 48 (3), pp. 414–427.
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23: Bibliography V
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Integrating products of Bessel functions with an additional exponential or rational factor.
Comput. Phys. Comm. 178 (8), pp. 578–590.
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Some novel infinite series of spherical Bessel functions.
Quart. Appl. Math. 42 (3), pp. 321–324.
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On the localization and computation of zeros of Bessel functions.
Z. Angew. Math. Mech. 77 (6), pp. 467–475.
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RFSFNS: A portable package for the numerical determination of the number and the calculation of roots of Bessel functions.
Comput. Phys. Comm. 92 (2-3), pp. 252–266.
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The topological degree theory for the localization and computation of complex zeros of Bessel functions.
Numer. Funct. Anal. Optim. 18 (1-2), pp. 227–234.
24: Software Index
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►‘✓’ indicates that a software package implements the functions in a section; ‘a’ indicates available functionality through optional or add-on packages; an empty space indicates no known support.
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►In the list below we identify four main sources of software for computing special functions.
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Commercial Software.
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►The following are web-based software repositories with significant holdings in the area of special functions.
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Open Source | With Book | Commercial | |||||||||||||||||||||||
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20 Theta Functions | |||||||||||||||||||||||||
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Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.
25: Bibliography W
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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Rational approximations for the modified Bessel function of the second kind.
Comput. Phys. Comm. 59 (3), pp. 471–493.
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Tables of Summable Series and Integrals Involving Bessel Functions.
Holden-Day, San Francisco, CA.
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Algorithm 44: Bessel functions computed recursively.
Comm. ACM 4 (4), pp. 177–178.
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The asymptotic expansion of the generalized Bessel function.
Proc. London Math. Soc. (2) 38, pp. 257–270.
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