elementary%20functions
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11: 12.10 Uniform Asymptotic Expansions for Large Parameter
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►With the upper sign in (12.10.2), expansions can be constructed for large in terms of elementary functions that are uniform for (§2.8(ii)).
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►The turning points can be included if expansions in terms of Airy functions are used instead of elementary functions (§2.8(iii)).
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§12.10(ii) Negative ,
… ►§12.10(vi) Modifications of Expansions in Elementary Functions
… ►12: 32.8 Rational Solutions
13: 30.9 Asymptotic Approximations and Expansions
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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
…14: Bibliography N
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Numerical Algorithms Group, Ltd..
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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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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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15: 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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4 Elementary 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.