Struve%20functions
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1: 11.14 Tables
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§11.14(ii) Struve Functions
… βΊZhang and Jin (1996) tabulates and for and to 8D or 7S.
§11.14(iii) Integrals
… βΊ§11.14(v) Incomplete Functions
βΊAgrest and Maksimov (1971, Chapter 11) defines incomplete Struve, Anger, and Weber functions and includes tables of an incomplete Struve function for , , and , together with surface plots.
2: Bibliography S
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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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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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The real zeros of Struve’s function.
SIAM J. Math. Anal. 1 (3), pp. 365–375.
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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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3: 11.6 Asymptotic Expansions
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§11.6(i) Large , Fixed
… βΊFor the corresponding expansions for and combine (11.6.1), (11.6.2) with (11.2.5), (11.2.6), (10.17.4), and (10.40.1). … βΊ§11.6(ii) Large , Fixed
… βΊ … βΊFor the corresponding result for use (11.2.5) and (10.19.6). …4: Bibliography N
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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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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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Approximations for the Bessel and Struve functions.
Math. Comp. 43 (168), pp. 551–556.
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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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Hypergeometric functions.
Acta Math. 94, pp. 289–349.
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5: Bibliography M
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Chebyshev expansions for modified Struve and related functions.
Math. Comp. 60 (202), pp. 735–747.
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems.
Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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6: Bibliography
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Efficient approximation of the Struve functions
occurring in the calculation of sound radiation quantities.
The Journal of the Acoustical Society of America 140 (6), pp. 4154–4160.
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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Tablitsy funktsii Struve i integralov ot nikh.
“Nauka”, Moscow (Russian).
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Derivatives and integrals with respect to the order of the Struve functions
and
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J. Math. Anal. Appl. 137 (1), pp. 17–36.
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7: Software Index
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βΊ‘β’ 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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βΊIn the list below we identify four main sources of software for computing special functions.
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Commercial Software.
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βΊThe 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.
8: Bibliography B
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A program for computing the Riemann zeta function for complex argument.
Comput. Phys. Comm. 20 (3), pp. 441–445.
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Integral representations and summations of the modified Struve function.
Acta Math. Hungar. 141 (3), pp. 254–281.
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Tables of modified Struve functions of orders zero and unity.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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On the derivatives of the Bessel and Struve functions with respect to the order.
Integral Transforms Spec. Funct. 16 (3), pp. 187–198.
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