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1: 35.1 Special Notation

… ►An alternative notation for the multivariate gamma function is ${\mathrm{\Pi }}_m(a)={\mathrm{\Gamma }}_m\left(a+\frac{1}{2}(m+1)\right)$ (Herz (1955, p. 480)). …

2: 20.9 Relations to Other Functions

… ►The relations (20.9.1) and (20.9.2) between $k$ and $\tau$ (or $q$) are solutions of Jacobi’s inversion problem; see Baker (1995) and Whittaker and Watson (1927, pp. 480–485). …

3: Bibliography V

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Expansions in products of Heine-Stieltjes polynomials. Constr. Approx. 15 (4), pp. 467–480.

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External Links:

ISSN 0176-4276, Document, MathReview (Luoqing Li), ZentralBlatt

Referenced by:

§31.15(iii).

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4: Bibliography

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Recurrence relations for the Fresnel integral ${\int }_0^{\mathrm{\infty }}\frac{\exp (-ct)dt}{\sqrt{t}(1+t^2)}$ and similar integrals. Comm. ACM 17 (8), pp. 480–481.

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External Links:

ISSN 0001-0782, Document, MathReview, ZentralBlatt

Referenced by:

§6.18(ii).

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Algorithm 609. A portable FORTRAN subroutine for the Bickley functions ${\mathrm{Ki}}_n(x)$ . ACM Trans. Math. Software 9 (4), pp. 480–493.

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Notes:

Single-precision Fortran, maximum accuracy 18S.

External Links:

ISSN 0098-3500, Document, GAMS (module 609; package TOMS), MathReview (Marietta J. Tretter), ZentralBlatt

Referenced by:

1st item.

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5: Bibliography S

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Asymptotic expansion of Mellin transforms in the complex plane. Int. J. Pure Appl. Math. 71 (3), pp. 465–480.

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External Links:

ISSN 1311-8080, MathReview Entry, ZentralBlatt

Referenced by:

§2.3(vi).

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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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Notes:

Sinc-Pack, a set of 480 Matlab programs with a 470-page tutorial, is available for purchase from SINC, LLC by contacting Frank Stenger.

External Links:

ISBN 0-387-94008-1, MathReview (B. Boyanov), ZentralBlatt

Referenced by:

§3.3(vi), §3.4(i), §3.5(i).

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6: 18.5 Explicit Representations

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$H_6\left(x\right)=64x^6-480x^4+720x^2-120.$

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7: Bibliography G

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Algorithm 236: Bessel functions of the first kind. Comm. ACM 7 (8), pp. 479–480.

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Notes:

For certification see same journal 8(1965), pp. 105–106, for remark see ACM Trans. Math. Software, 1(1975), pp. 282–284. Includes Algol program, maximum accuracy: 11D.

External Links:

ISSN 0001-0782, Document

Referenced by:

§10.77(iii).

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8: Bibliography C

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Landen Transformations of Integrals. In Asymptotic and Computational Analysis (Winnipeg, MB, 1989), R. Wong (Ed.), Lecture Notes in Pure and Appl. Math., Vol. 124, pp. 75–94.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§19.22(iii).

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