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21: Bibliography F
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Tables of Values of the Function for Complex Argument.
Edited by V. A. Fok; translated from the Russian by D. G. Fry.
Mathematical Tables Series, Vol. 11, Pergamon Press, Oxford.
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Polynomial relations in the Heisenberg algebra.
J. Math. Phys. 35 (11), pp. 6144–6149.
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On a unified approach to transformations and elementary solutions of Painlevé equations.
J. Math. Phys. 23 (11), pp. 2033–2042.
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Application of the -function theory of Painlevé equations to random matrices: , the JUE, CyUE, cJUE and scaled limits.
Nagoya Math. J. 174, pp. 29–114.
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Algorithm 435: Modified incomplete gamma function.
Comm. ACM 15 (11), pp. 993–995.
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22: Bibliography W
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Rapid approximation to the Voigt/Faddeeva function and its derivatives.
J. Quant. Spect. and Rad. Transfer 62 (1), pp. 29–48.
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Some hypergeometric orthogonal polynomials.
SIAM J. Math. Anal. 11 (4), pp. 690–701.
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On the zeros of a confluent hypergeometric function.
Proc. Amer. Math. Soc. 16 (2), pp. 281–283.
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On the asymptotic behavior of the Fourier coefficients of Mathieu functions.
J. Res. Nat. Inst. Standards Tech. 113 (1), pp. 11–15.
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The generalized Bessel function of order greater than one.
Quart. J. Math., Oxford Ser. 11, pp. 36–48.
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23: Bibliography S
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On integral representations for Lamé and other special functions.
SIAM J. Math. Anal. 11 (4), pp. 702–723.
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The Laplace transforms of products of Airy functions.
Dirāsāt Ser. B Pure Appl. Sci. 19 (2), pp. 7–11.
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A simple approach to asymptotic expansions for Fourier integrals of singular functions.
Appl. Math. Comput. 216 (11), pp. 3378–3385.
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Représentation asymptotique de la solution générale de l’équation de Mathieu-Hill.
Acad. Roy. Belg. Bull. Cl. Sci. (5) 51 (11), pp. 1415–1446.
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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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24: 34.7 Basic Properties: Symbol
25: Bibliography E
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The penetration of a potential barrier by electrons.
Phys. Rev. 35 (11), pp. 1303–1309.
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Higher Transcendental Functions. Vol. II.
McGraw-Hill Book Company, Inc., New York-Toronto-London.
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Painlevé transcendent describes quantum correlation function of the antiferromagnet away from the free-fermion point.
J. Phys. A 29 (17), pp. 5619–5626.
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Institutiones Calculi Integralis.
Opera Omnia (1), Vol. 11, pp. 110–113.
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26: 10.75 Tables
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Makinouchi (1966) tabulates all values of and in the interval , with at least 29S. These are for , 10, 20; , ; with and , except for .
Abramowitz and Stegun (1964, Chapter 11) tabulates , , , 10D; , , , 8D.
Leung and Ghaderpanah (1979), tabulates all zeros of the principal value of , for , 29S.
Abramowitz and Stegun (1964, Chapter 11) tabulates , , , 7D; , , , 6D.
Bickley and Nayler (1935) tabulates (§10.43(iii)) for , 2, 3, 9D.
27: Bibliography C
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Note on Nörlund’s polynomial
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Proc. Amer. Math. Soc. 11 (3), pp. 452–455.
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The fourth Painlevé equation and associated special polynomials.
J. Math. Phys. 44 (11), pp. 5350–5374.
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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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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Exact elliptic compactons in generalized Korteweg-de Vries equations.
Complexity 11 (6), pp. 30–34.
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28: Bibliography K
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Bernstein, Pick, Poisson and related integral expressions for Lambert
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Integral Transforms Spec. Funct. 23 (11), pp. 817–829.
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Auxiliary table for the incomplete elliptic integrals.
J. Math. Physics 27, pp. 11–36.
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Gravitational field of a spinning mass as an example of algebraically special metrics.
Phys. Rev. Lett. 11 (5), pp. 237–238.
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Algorithm 327: Dilogarithm [S22].
Comm. ACM 11 (4), pp. 270–271.
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Fractional integral and generalized Stieltjes transforms for hypergeometric functions as transmutation operators.
SIGMA Symmetry Integrability Geom. Methods Appl. 11, pp. Paper 074, 22.
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29: 2.2 Transcendental Equations
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►Conditions for the validity of the reversion process in are derived in Olver (1997b, pp. 14–16).
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30: Bibliography M
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Rational solutions of the Painlevé VI equation.
J. Phys. A 34 (11), pp. 2281–2294.
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Calculation of the complete elliptic integrals with complex modulus.
Numer. Math. 29 (2), pp. 233–236.
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Stirling numbers of the second kind.
Duke Math. J. 25 (1), pp. 29–43.
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Spheroidal eigenfunctions of the tidal equation.
Phys. Rev. Lett. 73 (11), pp. 1557–1560.
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Zeros of the function
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Differential Equations 11, pp. 797–811.
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