%E6%B2%99%E5%B7%B4%E4%BD%93%E8%82%B2%E6%8A%95%E6%B3%A8%E5%B9%B3%E5%8F%B0,%E6%B2%99%E5%B7%B4%E4%BD%93%E8%82%B2%E5%AE%98%E7%BD%91,%E3%80%90%E6%B2%99%E5%B7%B4%E4%BD%93%E8%82%B2%E6%8A%95%E6%B3%A8%E7%BD%91%E5%9D%80%E2%88%B63399yule.com%E3%80%91%E6%B2%99%E5%B7%B4%E4%BD%93%E8%82%B2%E8%B5%8C%E7%90%83%E5%B9%B3%E5%8F%B0,%E6%B2%99%E5%B7%B4%E4%BD%93%E8%82%B2%E7%BB%B4%E5%9F%BA%E7%99%BE%E7%A7%91,%E6%B2%99%E5%B7%B4%E4%BD%93%E8%82%B2app,%E6%B2%99%E5%B7%B4%E4%BD%93%E8%82%B2%E6%98%AF%E4%BB%80%E4%B9%88,%E6%B2%99%E5%B7%B4%E4%BD%93%E8%82%B2api,%E6%B2%99%E5%B7%B4%E4%B9%B0%E7%90%83%E5%B9%B3%E5%8F%B0%E3%80%90%E8%B5%8C%E7%90%83%E7%BD%91%E7%AB%99%E2%88%B63399yule.com%E3%80%91

SearchAdvancedHelp

Did you mean %E6%B2%99%E5%B7%B4%E4%BD%93%E8%82%B2%E6%8A%95%E6%B3%A8%E5%B9%B3%E5%8F%B0,%E6%B2%99%E5%B7%B4%E4%BD%93%E8%82%B2%E5%AE%98%E7%BD%91,%E3%80%90%E6%B2%99%E5%B7%B4%E4%BD%93%E8%82%B2%E6%8A%95%E6%B3%A8%E7%BD%91%E5%9D%80%E2%88%33929%E3%80%91%E6%B2%99%E5%B7%B4%E4%BD%93%E8%82%B2%E8%B5%8C%E7%90%83%E5%B9%B3%E5%8F%B0,%E6%B2%99%E5%B7%B4%E4%BD%93%E8%82%B2%E7%BB%B4%E5%9F%BA%E7%99%BE%E7%A7%91,%E6%B2%99%E5%B7%B4%E4%BD%93%E8%82%papp,%E6%B2%99%E5%B7%B4%E4%BD%93%E8%82%B2%E6%98%AF%E4%BB%80%E4%B9%88,%E6%B2%99%E5%B7%B4%E4%BD%93%E8%82%rapid,%E6%B2%99%E5%B7%B4%E4%B9%B0%E7%90%83%E5%B9%B3%E5%8F%B0%E3%80%90%E8%B5%8C%E7%90%83%E7%BD%91%E7%AB%99%E2%88%33929%E3%80%91 ?

(0.062 seconds)

1—10 of 729 matching pages

1: 34.13 Methods of Computation

… ►Methods of computation for $\mathit{3}j$ and $\mathit{6}j$ symbols include recursion relations, see Schulten and Gordon (1975a), Luscombe and Luban (1998), and Edmonds (1974, pp. 42–45, 48–51, 97–99); summation of single-sum expressions for these symbols, see Varshalovich et al. (1988, §§8.2.6, 9.2.1) and Fang and Shriner (1992); evaluation of the generalized hypergeometric functions of unit argument that represent these symbols, see Srinivasa Rao and Venkatesh (1978) and Srinivasa Rao (1981). ►For $\mathit{9}j$ symbols, methods include evaluation of the single-sum series (34.6.2), see Fang and Shriner (1992); evaluation of triple-sum series, see Varshalovich et al. (1988, §10.2.1) and Srinivasa Rao et al. (1989). …

2: Bibliography

… ►

Some determinants of Bernoulli, Euler and related numbers. Portugal. Math. 18, pp. 91–99.

ⓘ

External Links:

FullText, MathReview (D. P. Banerjee), ZentralBlatt

Referenced by:

§24.14(ii).

Encodings:

BibTeX

… ►

Algorithm 683: A portable FORTRAN subroutine for exponential integrals of a complex argument. ACM Trans. Math. Software 16 (2), pp. 178–182.

ⓘ

Notes:

Double- and single-precision Fortran, maximum accuracy 18S or 14S.

External Links:

ISSN 0098-3500, Document, GAMS (module 683; package TOMS), MathReview, ZentralBlatt

Referenced by:

1st item, 1st item.

Encodings:

BibTeX

… ►

Applications of basic hypergeometric functions. SIAM Rev. 16 (4), pp. 441–484.

ⓘ

External Links:

Document, MathReview (L. J. Slater), ZentralBlatt

Referenced by:

§17.16, Ch.17.

Encodings:

BibTeX

… ►

Bernoulli’s power-sum formulas revisited. Math. Gaz. 90 (518), pp. 276–279.

ⓘ

Referenced by:

§24.4(iii).

Encodings:

BibTeX

… ►

Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters. J. Math. Anal. Appl. 416 (1), pp. 52–80.

ⓘ

External Links:

ISSN 0022-247X, Document, Link, MathReview (Vivek Sahai), ZentralBlatt

Referenced by:

§18.15(vi), §18.15(vi).

Encodings:

BibTeX

…

3: Publications

… ►

Design of a Digital Mathematical Library for Science, Technology and Education, Proceedings of the IEEE Forum on Research and Technology Advances in Digital Libraries (IEEE ADL ’99, Baltimore, Maryland, May 19, 1999).

… ►

The NIST Digital Library of Mathematical Functions Project, Annals of Mathematics and Artificial Intelligence—Special Issue on Mathematical Knowledge Management, Vol. 38, Nos. 1–3, pp. 105–119.

►

Technical Aspects of the Digital Library of Mathematical Functions, Annals of Mathematics and Artificial Intelligence—Special Issue on Mathematical Knowledge Management, Vol. 38, Nos. 1–3, pp. 121–136.

…

4: 18.13 Continued Fractions

… ►See also Cuyt et al. (2008, pp. 91–99).

5: Bibliography T

… ►

On the connection formula for the first Painlevé equation—from the viewpoint of the exact WKB analysis. Sūrikaisekikenkyūsho Kōkyūroku (931), pp. 70–99.

ⓘ

Notes:

Painlevé functions and asymptotic analysis (Japanese) (Kyoto, 1995)

External Links:

FullText, MathReview (Andrei A. Kapaev)

Referenced by:

§32.12(i).

Encodings:

BibTeX

… ►

LSFBTR: A subroutine for calculating spherical Bessel transforms. Comput. Phys. Comm. 30 (1), pp. 93–99.

ⓘ

Notes:

Single-precision Fortran.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

9th item.

Encodings:

BibTeX

… ►

The numerical computation of the confluent hypergeometric function $U(a,b,z)$ . Numer. Math. 41 (1), pp. 63–82.

ⓘ

Notes:

Algol 60 variable-precision procedures are included.

External Links:

ISSN 0029-599X, Document, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§13.29(iv), §13.32(ii).

Encodings:

BibTeX

… ►

Bernoulli polynomials old and new: Generalizations and asymptotics. CWI Quarterly 8 (1), pp. 47–66.

ⓘ

External Links:

ISSN 0922-5366, FullText, MathReview (Michael Hauss), ZentralBlatt

Referenced by:

§24.11, §24.16(i).

Encodings:

BibTeX

… ►

Atlas for Computing Mathematical Functions: An Illustrated Guide for Practitioners. John Wiley & Sons Inc., New York.

ⓘ

Notes:

With CD-ROM containing a large collection of mathematical function software written in Fortran 90 and Mathematica (an edition with the same software in C and Mathematica exists also). The functions are computed for real variables only. Maximum accuracy 12D.

External Links:

ISBN 0-471-18171-4, MathReview, ZentralBlatt

Referenced by:

§19.36(ii), § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

Encodings:

BibTeX

…

6: Bibliography C

… ►

Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams. J. Comput. Appl. Math. 115 (1-2), pp. 93–99.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (Lorenzo L. Salcedo), ZentralBlatt

Referenced by:

§16.24(ii).

Encodings:

BibTeX

… ►

Generalized incomplete gamma functions with applications. J. Comput. Appl. Math. 55 (1), pp. 99–124.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§8.16.

Encodings:

BibTeX

… ►

Chebyshev polynomial expansions of complete elliptic integrals. Math. Comp. 19 (90), pp. 249–259.

ⓘ

External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§19.38.

Encodings:

BibTeX

… ►

Numerical evaluation of Airy functions with complex arguments. J. Comput. Phys. 99 (1), pp. 106–114.

ⓘ

External Links:

ISSN 0021-9991, Document, MathReview, ZentralBlatt

Referenced by:

4th item, 1st item.

Encodings:

BibTeX

… ►

Zeros of the Hankel function of real order out of the principal Riemann sheet. J. Comput. Appl. Math. 37 (1-3), pp. 89–99.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.21(ix).

Encodings:

BibTeX

…

7: Bibliography K

… ►

A proof of the $q$-Macdonald-Morris conjecture for $B{C}_n$ . Mem. Amer. Math. Soc. 108 (516), pp. vi+80.

ⓘ

External Links:

ISSN 0065-9266, MathReview (Eric M. Opdam), ZentralBlatt

Referenced by:

§17.14.

Encodings:

BibTeX

… ►

Linear convergence and the bisection algorithm. Amer. Math. Monthly 93 (1), pp. 48–51.

ⓘ

External Links:

ISSN 0002-9890, FullText, MathReview (J. G. Herriot), ZentralBlatt

Referenced by:

§3.8(iii).

Encodings:

BibTeX

… ►

Algorithm 763: INTERVAL_ARITHMETIC: A Fortran 90 module for an interval data type. ACM Trans. Math. Software 22 (4), pp. 385–392.

ⓘ

External Links:

ISSN 0098-3500, Document, GAMS (module 763; package TOMS), ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX

… ►

Two notes on notation. Amer. Math. Monthly 99 (5), pp. 403–422.

ⓘ

External Links:

ISSN 0002-9890, FullText, MathReview (W. Dörfler), ZentralBlatt

Referenced by:

§26.1, §26.1, Notations, Notations.

Encodings:

BibTeX

… ►

Nonsymmetric Askey-Wilson polynomials as vector-valued polynomials. Appl. Anal. 90 (3-4), pp. 731–746.

ⓘ

External Links:

ISSN 0003-6811, Link, MathReview (Masatoshi Iida), ZentralBlatt

Referenced by:

§18.38(iii), §18.38(iii).

Encodings:

BibTeX

…

8: Bibliography N

… ►

Generalization of Binet’s Gamma function formulas. Integral Transforms Spec. Funct. 24 (8), pp. 597–606.

ⓘ

External Links:

ISSN 1065-2469, Document, FullText, MathReview (Daniele Ritelli), ZentralBlatt

Referenced by:

§5.11(i), §5.11(i).

Encodings:

BibTeX

… ►

Elliptic integrals of the second and third kinds. Zastos. Mat. 11, pp. 99–102.

ⓘ

Notes:

Includes Algol program.

External Links:

MathReview

Referenced by:

§19.39(iii).

Encodings:

BibTeX

… ►

Der Eulersche Dilogarithmus und seine Verallgemeinerungen. Nova Acta Leopoldina 90, pp. 123–212.

ⓘ

External Links:

ZentralBlatt

Referenced by:

§25.12(i).

Encodings:

BibTeX

… ►

The asymptotic behavior of the general real solution of the third Painlevé equation. Dokl. Akad. Nauk SSSR 283 (5), pp. 1161–1165 (Russian).

ⓘ

Notes:

In Russian. English translation: Sov. Math., Dokl. 30(1988), no. 8, pp. 666–668.

External Links:

ISSN 0002-3264, MathReview (Vojislav Marić), ZentralBlatt

Referenced by:

§32.11(iv).

Encodings:

BibTeX

… ►

ⓘ

Notes:

A large general purpose mathematical software collection containing some special function codes. Implementation is in single precision.

External Links:

Home Page

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

Encodings:

BibTeX

…

9: Bibliography I

… ►

Further investigations into the periodic Lamé functions. Proc. Roy. Soc. Edinburgh 60, pp. 83–99.

ⓘ

External Links:

MathReview (H. Bateman), ZentralBlatt

Referenced by:

§29.1, §29.17(ii), §29.3(iii), §29.6(i), §29.6(ii), §29.6(iii), §29.6(iv), Ch.29, Notations E, Notations E, Notations E, Notations E.

Encodings:

BibTeX

… ►

Classical and Quantum Orthogonal Polynomials in One Variable. Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.

ⓘ

External Links:

ISBN 978-0-521-78201-2; 0-521-78201-5, MathReview Entry, ZentralBlatt

Referenced by:

§1.4(v), Profile Mourad E.H. Ismail, Erratum (V1.0.20) for Chapter 18 Orthogonal Polynomials.

Encodings:

BibTeX

►

Classical and Quantum Orthogonal Polynomials in One Variable. Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.

ⓘ

Notes:

With two chapters by Walter Van Assche, With a foreword by Richard A. Askey, Corrected reprint of the 2005 original.

External Links:

ISBN 978-0-521-14347-9, MathReview Entry, ZentralBlatt

Referenced by:

§18.12, (18.15.4_5), (18.16.19), (18.16.20), (18.16.21), §18.17(ii), §18.18(vii), §18.19, (18.2.20), §18.2(vi), §18.2(xii), §18.2(xii), §18.2(x), §18.20(i), §18.20(ii), §18.21(ii), §18.22(i), §18.22(ii), §18.22(iii), §18.23, §18.25(i), §18.25(iii), §18.26(i), §18.26(iv), (18.27.4), §18.27(i), §18.27(ii), §18.27(iii), §18.27(v), §18.27(vi), §18.28(i), §18.28(ii), §18.28(iii), §18.28(v), §18.28(vi), §18.28(vii), §18.28(viii), §18.30(vi), §18.30(vii), §18.30(iii), §18.30(iv), §18.30, §18.30(vi), §18.34(i), §18.34(ii), §18.34(ii), §18.34(iii), (18.35.4), (18.35.5), (18.35.6), (18.35.6_2), (18.35.6_3), (18.35.6_4), (18.35.7), (18.35.8), §18.35(ii), §18.35(iii), §18.36(iii), §18.38(ii), §18.39(iv), §18.39(iv), §18.39(iv), (18.40.4), Profile Mourad E.H. Ismail, Erratum (V1.0.20) for Chapter 18 Orthogonal Polynomials.

Encodings:

BibTeX

…

10: Bibliography E

… ►

Some recent results on the zeros of Bessel functions and orthogonal polynomials. J. Comput. Appl. Math. 133 (1-2), pp. 65–83.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (N. Hayek Calil), ZentralBlatt

Referenced by:

§10.21(iv).

Encodings:

BibTeX

… ►

The Fuchsian equation of second order with four singularities. Duke Math. J. 9 (1), pp. 48–58.

ⓘ

External Links:

Document, MathReview (R. E. Langer), ZentralBlatt

Referenced by:

§31.11(i).

Encodings:

BibTeX

… ►

Algorithm 934: Fortran 90 subroutines to compute Mathieu functions for complex values of the parameter. ACM Trans. Math. Softw. 40 (1), pp. 8:1–8:19.

ⓘ

External Links:

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

Referenced by:

4th item, §28.36(iii).

Encodings:

BibTeX

►

Algorithm 861: Fortran 90 subroutines for computing the expansion coefficients of Mathieu functions using Blanch’s algorithm. ACM Trans. Math. Software 32 (4), pp. 622–634.

ⓘ

External Links:

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

Referenced by:

3rd item, §28.36(iii).

Encodings:

BibTeX

… ►

The asymptotic behaviour of the inhomogeneous Airy function $\mathrm{Hi}(z)$ . Math. Chronicle 12, pp. 99–104.

ⓘ

External Links:

ISSN 0581-1155, MathReview (Ram Kishore Saxena), ZentralBlatt

Referenced by:

(9.12.24), §9.12(vii).

Encodings:

BibTeX