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1: 12.10 Uniform Asymptotic Expansions for Large Parameter
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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(vi) Modifications of Expansions in Elementary Functions
… ►Modified Expansions
… ►§12.10(viii) Negative , . Expansions in Terms of Airy Functions
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Asymptotic expansions of the modified Bessel function of the third kind of imaginary order.
SIAM J. Appl. Math. 15, pp. 1315–1323.
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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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Asymptotic expansions for the coefficient functions that arise in turning-point problems.
Proc. Roy. Soc. London Ser. A 410, pp. 35–60.
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Asymptotic Expansions for the Coefficient Functions Associated with Linear Second-order Differential Equations: The Simple Pole Case.
In Asymptotic and Computational Analysis (Winnipeg, MB, 1989), R. Wong (Ed.),
Lecture Notes in Pure and Applied Mathematics, Vol. 124, pp. 53–73.
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3: Bibliography S
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On the expansion of the parabolic cylinder function in a series of the product of two parabolic cylinder functions.
J. Indian Math. Soc. (N. S.) 3, pp. 226–230.
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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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Uniform asymptotic expansions of modified Mathieu functions.
J. Reine Angew. Math. 247, pp. 1–17.
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Exact error terms in the asymptotic expansion of a class of integral transforms. I. Oscillatory kernels.
SIAM J. Math. Anal. 11 (5), pp. 828–841.
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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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4: Bibliography C
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Expansions in terms of parabolic cylinder functions.
Proc. Edinburgh Math. Soc. (2) 8, pp. 50–65.
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Chebyshev expansions for the Bessel function
in the complex plane.
Math. Comp. 40 (161), pp. 343–366.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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On the asymptotic expansion of Airy’s integral.
Proc. Glasgow Math. Assoc. 6, pp. 113–115.
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5: Bibliography G
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Computation of Bessel and Airy functions and of related Gaussian quadrature formulae.
BIT 42 (1), pp. 110–118.
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Problem 72-21, Laplace transforms of Airy functions.
SIAM Rev. 15 (4), pp. 796–798.
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On nonoscillating integrals for computing inhomogeneous Airy functions.
Math. Comp. 70 (235), pp. 1183–1194.
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Computation of the modified Bessel function of the third kind of imaginary orders: Uniform Airy-type asymptotic expansion.
J. Comput. Appl. Math. 153 (1-2), pp. 225–234.
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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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6: 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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Two-point quasi-fractional approximations to the Airy function
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J. Comput. Phys. 99 (2), pp. 337–340.
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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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The Second Painlevé Transcendent: A Nonlinear Airy Function.
In Mechanics Today,
Vol. 5, pp. 297–313.
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Asymptotic expansions of ellipsoidal wave functions in terms of Hermite functions.
Math. Nachr. 32, pp. 49–62.
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