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1: Bibliography S

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A property of the zeros of cross-product Bessel functions of different orders. Z. Angew. Math. Mech. 56 (2), pp. 120–121.

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External Links:

Document, MathReview (S. Saran), ZentralBlatt

Referenced by:

§10.21(x).

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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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External Links:

ZentralBlatt

Referenced by:

§12.13(i).

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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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External Links:

Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§28.8(iv).

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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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External Links:

ISSN 0253-424X, MathReview

Referenced by:

§9.10(v).

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Algorithm AS 239. Chi-squared and incomplete gamma integral. Appl. Statist. 37 (3), pp. 466–473.

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Notes:

Double-precision Fortran.

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FullText, Code

Referenced by:

5th item.

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2: 20.7 Identities

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§20.7(i) Sums of Squares

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§20.7(iv) Reduction Formulas for Products

… ►See Lawden (1989, pp. 19–20). … ►In the following equations ${\tau }^{\prime }=-1/\tau$, and all square roots assume their principal values. … ►

§20.7(ix) Addendum to 20.7(iv) Reduction Formulas for Products

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3: Bibliography M

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On the zeros of cross-product Bessel functions. J. Math. Mech. 16, pp. 447–452.

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External Links:

MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.21(x).

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Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions. Ramanujan J. 6 (1), pp. 7–149.

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External Links:

Document, ZentralBlatt

Referenced by:

§27.13(iv).

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New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function. Proc. Nat. Acad. Sci. U.S.A. 93 (26), pp. 15004–15008.

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ISSN 0027-8424, MathReview (Ken Ono), ZentralBlatt

Referenced by:

§27.13(iv).

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The $q$-analogue of the Laguerre polynomials. J. Math. Anal. Appl. 81 (1), pp. 20–47.

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ISSN 0022-247X, Document, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.27(v).

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On the representation of numbers as a sum of $2r$ squares. Quarterly Journal of Math. 48, pp. 93–104.

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ZentralBlatt

Referenced by:

§27.13(iv).

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4: 26.12 Plane Partitions

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26.12.9 $${\left(\prod _{h=1}^r\prod _{j=1}^s\frac{h+j+t-1}{h+j-1}\right)}^2;$$

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Symbols:

$r$: positive integer, $s$: positive integer, $t$: positive integer, $h$: positive integer and $j$: positive integer

Permalink:

http://dlmf.nist.gov/26.12.E9

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See also:

Annotations for §26.12(i), §26.12 and Ch.26

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26.12.10 $$\left(\prod _{h=1}^r\prod _{j=1}^s\frac{h+j+t-1}{h+j-1}\right)\left(\prod _{h=1}^{r+1}\prod _{j=1}^s\frac{h+j+t-1}{h+j-1}\right);$$

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Symbols:

$r$: positive integer, $s$: positive integer, $t$: positive integer, $h$: positive integer and $j$: positive integer

Permalink:

http://dlmf.nist.gov/26.12.E10

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See also:

Annotations for §26.12(i), §26.12 and Ch.26

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26.12.11 $$\left(\prod _{h=1}^{r+1}\prod _{j=1}^s\frac{h+j+t-1}{h+j-1}\right)\left(\prod _{h=1}^r\prod _{j=1}^{s+1}\frac{h+j+t-1}{h+j-1}\right).$$

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Symbols:

$r$: positive integer, $s$: positive integer, $t$: positive integer, $h$: positive integer and $j$: positive integer

Permalink:

http://dlmf.nist.gov/26.12.E11

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Annotations for §26.12(i), §26.12 and Ch.26

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26.12.13 $$\prod _{h=1}^r\prod _{j=1}^r\frac{h+j+t-1}{h+j-1};$$

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Symbols:

$r$: positive integer, $t$: positive integer, $h$: positive integer and $j$: positive integer

Permalink:

http://dlmf.nist.gov/26.12.E13

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See also:

Annotations for §26.12(i), §26.12 and Ch.26

… ►where ${\sigma }_2(j)$ is the sum of the squares of the divisors of $j$. …

5: Bibliography B

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Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.

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External Links:

Document

Referenced by:

§33.22(iv).

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Products of generalized hypergeometric series. Proc. London Math. Soc. (2) 28 (2), pp. 242–254.

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External Links:

Document, ZentralBlatt

Referenced by:

§16.12.

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Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.

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Notes:

Double-precision Fortran code.

External Links:

Document, Code

Referenced by:

1st item, 4th item.

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Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.

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External Links:

Document, ZentralBlatt

Referenced by:

§10.73(iv).

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Numerical Methods for Least Squares Problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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External Links:

ISBN 0-89871-360-9, MathReview (Hongyuan Zha), ZentralBlatt

Referenced by:

§3.11(v).

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BibTeX

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6: Bibliography K

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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.

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External Links:

ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt

Referenced by:

1st item.

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Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

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External Links:

Document, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.18(i).

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Tables of the Incomplete Gamma Function Ratio: The Chi-square Integral, the Poisson Distribution. Justus von Liebig Verlag, Darmstadt (German, English).

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Notes:

In cooperation with W. Rudert

External Links:

MathReview, ZentralBlatt

Referenced by:

1st item.

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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.

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ISSN 0266-5611, Document, MathReview (Shun Shimomura), ZentralBlatt

Referenced by:

§32.11(iv).

Encodings:

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Jacobi polynomials. II. An analytic proof of the product formula. SIAM J. Math. Anal. 5, pp. 125–137.

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External Links:

Document, MathReview (R. P. Soni), ZentralBlatt

Referenced by:

§18.12, §18.17(ii), §18.18(vi).

Encodings:

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