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11: 12.10 Uniform Asymptotic Expansions for Large Parameter
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►These cases are treated in §§12.10(vii)–12.10(viii).
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►For
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§12.10(vii) Negative , . Expansions in Terms of Airy Functions
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12.10.40
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12.10.41
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12: 9.10 Integrals
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9.10.6
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§9.10(vii) Stieltjes Transforms
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9.10.18
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9.10.19
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►For further integrals, including the Airy transform, see §9.11(iv), Widder (1979), Prudnikov et al. (1990, §1.8.1), Prudnikov et al. (1992a, pp. 405–413), Prudnikov et al. (1992b, §4.3.25), Vallée and Soares (2010, Chapters 3, 4).
13: 18.16 Zeros
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►except when .
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18.16.7
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18.16.11
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►In the notation of this reference , , and .
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§18.16(vii) Discriminants
…14: 28.4 Fourier Series
15: 32.7 Bäcklund Transformations
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►Next, let , , be solutions of with
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►Let and , , be solutions of with
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§32.7(vii) Sixth Painlevé Equation
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32.7.50
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16: 4 Elementary Functions
Chapter 4 Elementary Functions
…17: Errata
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Equations (22.9.8), (22.9.9) and (22.9.10)
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Version 1.0.25 (December 15, 2019)
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22.9.8
22.9.9
22.9.10
Originally all the functions , , and in Equations (22.9.8), (22.9.9) and (22.9.10) were written incorrectly with . These functions have been corrected so that they are written with . In the sentence just below (22.9.10), the expression has been corrected to read .
Reported by Juan Miguel Nieto on 2019-11-07
Version 1.0.24 (September 15, 2019)
… ►Version 1.0.23 (June 15, 2019)
… ►Version 1.0.22 (March 15, 2019)
…18: Bibliography Q
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Asymptotic expansion of the Krawtchouk polynomials and their zeros.
Comput. Methods Funct. Theory 4 (1), pp. 189–226.
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“Best possible” upper and lower bounds for the zeros of the Bessel function
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Trans. Amer. Math. Soc. 351 (7), pp. 2833–2859.
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19: 22.9 Cyclic Identities
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►These identities are cyclic in the sense that each of the indices in the first product of, for example, the form are simultaneously permuted in the cyclic order: ; .
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22.9.17
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22.9.18
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§22.9(iv) Typical Identities of Rank 4
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22.9.23
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20: Bibliography T
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Zonal Polynomials.
Institute of Mathematical Statistics Lecture Notes—Monograph
Series, 4, Institute of Mathematical Statistics, Hayward, CA.
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The asymptotic expansion of the incomplete gamma functions.
SIAM J. Math. Anal. 10 (4), pp. 757–766.
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Six myths of polynomial interpolation and quadrature.
Math. Today (Southend-on-Sea) 47 (4), pp. 184–188.
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Sul comportamento asintotico dell’-esimo polinomio di Laguerre nell’intorno dell’ascissa
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Comment. Math. Helv. 22, pp. 150–167.
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Theory of the Fresnel integral.
USSR Comput. Math. and Math. Phys. 9 (4), pp. 271–279.