infinite%20series

SearchAdvancedHelp

(0.002 seconds)

11—16 of 16 matching pages

11: Bibliography V

… ►

On the series expansion method for computing incomplete elliptic integrals of the first and second kinds. Math. Comp. 23 (105), pp. 61–69.

ⓘ

External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§19.12, §19.5.

Encodings:

BibTeX

… ►

An infinite series of Weber’s parabolic cylinder functions. Proc. Benares Math. Soc. (N.S.) 3, pp. 37.

ⓘ

External Links:

MathReview (M. C. Gray), ZentralBlatt

Referenced by:

§12.13(ii).

Encodings:

BibTeX

… ►

Some novel infinite series of spherical Bessel functions. Quart. Appl. Math. 42 (3), pp. 321–324.

ⓘ

External Links:

ISSN 0033-569X, MathReview (A. de Castro Brzezicki), ZentralBlatt

Referenced by:

§10.60(iii), §10.60(iii).

Encodings:

BibTeX

… ►

Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation. Constr. Approx. 20 (1), pp. 39–54.

ⓘ

External Links:

ISSN 0176-4276, Document, MathReview, ZentralBlatt

Referenced by:

§30.16(i), §30.16(ii), §30.16(ii).

Encodings:

BibTeX

… ►

Fourier series representation of Ferrers function $𝖯$ .

ⓘ

External Links:

FullText

Referenced by:

(14.13.1).

Encodings:

BibTeX

…

12: Bibliography C

… ►

Power series for inverse Jacobian elliptic functions. Math. Comp. 77 (263), pp. 1615–1621.

ⓘ

External Links:

ISSN 0025-5718, Document, MathReview (Shaun Cooper), ZentralBlatt

Referenced by:

§19.25(v), §22.15(ii).

Encodings:

BibTeX

… ►

Introduction to the Theory of Fourier’s Series and Integrals. 3rd edition, Macmillan, London.

ⓘ

Notes:

Reprinted by Dover, New York, 1950.

External Links:

ZentralBlatt

Referenced by:

§6.16(i).

Encodings:

BibTeX

… ►

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

ⓘ

External Links:

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

Referenced by:

§26.8(vii).

Encodings:

BibTeX

… ►

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

ⓘ

External Links:

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

Referenced by:

§13.29(v), §15.19(v).

Encodings:

BibTeX

… ►

Coulomb effects in the Klein-Gordon equation for pions. Phys. Rev. C 20 (2), pp. 696–704.

ⓘ

External Links:

Document

Referenced by:

5th item.

Encodings:

BibTeX

…

13: Bibliography I

… ►

The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of $J_0(z)-i{J}_1(z)$ and of Bessel functions $J_m(z)$ of any real order $m$ . Linear Algebra Appl. 194, pp. 35–70.

ⓘ

External Links:

ISSN 0024-3795, Document, MathReview (Alan L. Andrew), ZentralBlatt

Referenced by:

§10.21(ix).

Encodings:

BibTeX

… ►

The real roots of Bernoulli polynomials. Ann. Univ. Turku. Ser. A I 37, pp. 1–20.

ⓘ

External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.12(i).

Encodings:

BibTeX

… ►

Special Functions, $q$-Series and Related Topics. Fields Institute Communications, Vol. 14, American Mathematical Society, Providence, RI.

ⓘ

External Links:

ISBN 0-8218-0524-X, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

Profile Mourad E.H. Ismail.

Encodings:

BibTeX

… ►

$q$-Series from a Contemporary Perspective. Contemporary Mathematics, Vol. 254, American Mathematical Society, Providence, RI.

ⓘ

External Links:

ISBN 0-8218-1150-9, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

Profile Mourad E.H. Ismail.

Encodings:

BibTeX

… ►

Quantum Field Theory. International Series in Pure and Applied Physics, McGraw-Hill International Book Co., New York.

ⓘ

Notes:

Reprinted by Dover, 2006.

External Links:

ISBN 0-07-032071-3, MathReview (V. E. Korepin)

Referenced by:

§22.19(ii).

Encodings:

BibTeX

…

14: Bibliography O

… ►

Summing one- and two-dimensional series related to the Euler series. J. Comput. Appl. Math. 98 (2), pp. 245–271.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (Boris Petrovich Osilenker), ZentralBlatt

Referenced by:

§25.8.

Encodings:

BibTeX

… ►

Complete elliptic integrals resulting from infinite integrals of Bessel functions. J. Res. Nat. Bur. Standards Sect. B 78B (3), pp. 113–135.

ⓘ

External Links:

ISSN 0160-1741, MathReview (Y. L. Luke), ZentralBlatt

Referenced by:

§10.22(vi), §10.43(vi).

Encodings:

BibTeX

►

Complete elliptic integrals resulting from infinite integrals of Bessel functions. II. J. Res. Nat. Bur. Standards Sect. B 79B (3-4), pp. 137–170.

ⓘ

External Links:

ISSN 0160-1741, MathReview (Y. L. Luke), ZentralBlatt

Referenced by:

§10.22(vi), §10.43(vi).

Encodings:

BibTeX

… ►

An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series. J. Inst. Math. Appl. 20 (3), pp. 379–391.

ⓘ

External Links:

Document, MathReview (David L. Elliott), ZentralBlatt

Referenced by:

§3.11(ii).

Encodings:

BibTeX

… ►

A closed form solution of the $s$-wave Bethe-Goldstone equation with an infinite repulsive core. J. Math. Phys. 27 (4), pp. 1154–1158.

ⓘ

External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§30.13(v).

Encodings:

BibTeX

…

15: 25.11 Hurwitz Zeta Function

… ►The function $\zeta (s,a)$ was introduced in Hurwitz (1882) and defined by the series expansion … ►

§25.11(iv) Series Representations

… ►For other series expansions similar to (25.11.10) see Coffey (2008). … ►

§25.11(x) Further Series Representations

… ►

25.11.39 $$\sum _{k=2}^{\mathrm{\infty }}\frac{k}{2^k}\zeta (k+1,\frac{3}{4})=8G,$$

ⓘ

Symbols:

$\zeta (s,a)$: Hurwitz zeta function, $k$: nonnegative integer and $G$: Catalan’s constant

Keywords:

Catalan’s constant, infiniteseries

Source:

Adamchik and Srivastava (1998, (2.30), p. 138)

Permalink:

http://dlmf.nist.gov/25.11.E39

Encodings:

pMML, png, TeX

See also:

Annotations for §25.11(xi), §25.11 and Ch.25

…

16: Bibliography

… ►

Exact linearization of a Painlevé transcendent. Phys. Rev. Lett. 38 (20), pp. 1103–1106.

ⓘ

External Links:

Document, MathReview (Mark Adler)

Referenced by:

§32.11(ii), §32.13(i), §32.13(ii), §32.13(iii), §32.5.

Encodings:

BibTeX

… ►

There are infinitely many Carmichael numbers. Ann. of Math. (2) 139 (3), pp. 703–722.

ⓘ

External Links:

ISSN 0003-486X, FullText, MathReview (H. L. Montgomery), ZentralBlatt

Referenced by:

§27.12.

Encodings:

BibTeX

… ►

Summations and transformations for basic Appell series. J. London Math. Soc. (2) 4, pp. 618–622.

ⓘ

External Links:

MathReview (R. N. Jain), ZentralBlatt

Referenced by:

§17.11.

Encodings:

BibTeX

… ►

Multiple series Rogers-Ramanujan type identities. Pacific J. Math. 114 (2), pp. 267–283.

ⓘ

External Links:

ISSN 0030-8730, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§17.12.

Encodings:

BibTeX

… ►

Table of Definite and Infinite Integrals. Physical Sciences Data, Vol. 13, Elsevier Scientific Publishing Co., Amsterdam.

ⓘ

Notes:

Table errata: Math. Comp. v. 65 (1996), no. 215, p. 1386.

External Links:

ISBN 0-444-42151-3, MathReview (R. P. Boas), ZentralBlatt

Referenced by:

§1.4(iv), §10.22(vi), §10.43(vi), §11.7(v), §11.9(iv), §12.5(iv), §13.10(vi), §13.23(v), §15.14, §16.20, §16.5, §18.17(ix), §4.10(iii), §4.26(v), §4.40(v), §5.13, §6.14(iii), §7.14(iii), §8.14, §8.19(x).

Encodings:

BibTeX

…