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11: Bibliography C

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Asymptotic estimates for generalized Stirling numbers. Analysis (Munich) 20 (1), pp. 1–13.

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External Links:

ISSN 0174-4747, MathReview (F. T. Howard), ZentralBlatt

Referenced by:

§26.8(vii).

Encodings:

BibTeX

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Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

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External Links:

ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§13.29(v), §15.19(v).

Encodings:

BibTeX

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Molecular collisions and cusp catastrophes: Three methods for the calculation of Pearcey’s integral and its derivatives. Chem. Phys. Lett. 81 (2), pp. 306–310.

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External Links:

ISSN 0009-2614, Document, MathReview (J. S. Joel)

Referenced by:

§36.14(iii).

Encodings:

BibTeX

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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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External Links:

Document

Referenced by:

5th item.

Encodings:

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12: 23.18 Modular Transformations

… ►and $\lambda \left(\tau \right)$ is a cusp form of level zero for the corresponding subgroup of SL$(2,\mathbb{Z})$. …

13: 36.6 Scaling Relations

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Table 36.6.1: Special cases of scaling exponents for cuspoids.

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singularity	$K$	${\beta }_K$	${\gamma }_{1K}$	${\gamma }_{2K}$	${\gamma }_{3K}$	${\gamma }_K$
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cusp	2	$\frac{1}{4}$	$\frac{3}{4}$	$\frac{1}{2}$	$-$	$\frac{5}{4}$
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14: 8 Incomplete Gamma and Related
Functions

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15: 28 Mathieu Functions and Hill’s Equation

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16: 8.26 Tables

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Khamis (1965) tabulates $P(a,x)$ for $a=0.05(.05)10(.1)20(.25)70$, $0.0001\le x\le 250$ to 10D.

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Abramowitz and Stegun (1964, pp. 245–248) tabulates $E_n\left(x\right)$ for $n=2,3,4,10,20$, $x=0(.01)2$ to 7D; also $(x+n){\mathrm{e}}^x{E}_n\left(x\right)$ for $n=2,3,4,10,20$, $x^{-1}=0(.01)0.1(.05)0.5$ to 6S.

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Pagurova (1961) tabulates $E_n\left(x\right)$ for $n=0(1)20$, $x=0(.01)2(.1)10$ to 4-9S; ${\mathrm{e}}^x{E}_n\left(x\right)$ for $n=2(1)10$, $x=10(.1)20$ to 7D; ${\mathrm{e}}^x{E}_p\left(x\right)$ for $p=0(.1)1$, $x=0.01(.01)7(.05)12(.1)20$ to 7S or 7D.

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Zhang and Jin (1996, Table 19.1) tabulates $E_n\left(x\right)$ for $n=1,2,3,5,10,15,20$, $x=0(.1)1,1.5,2,3,5,10,20,30,50,100$ to 7D or 8S.

17: 23 Weierstrass Elliptic and Modular
Functions

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18: 36.10 Differential Equations

… ► $K=2$, cusp: … ► $K=2$, cusp: …

19: 36 Integrals with Coalescing Saddles

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20: Gergő Nemes

… ►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions. …