argument a fraction

SearchAdvancedHelp

(0.005 seconds)

21—26 of 26 matching pages

21: Bibliography K

… ►

Series expansions for the third incomplete elliptic integral via partial fraction decompositions. J. Comput. Appl. Math. 207 (2), pp. 331–337.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (José Luis López), ZentralBlatt

Referenced by:

§19.12, §19.5.

Encodings:

BibTeX

… ►

Algorithm 877: A subroutine package for cylindrical functions of complex order and nonnegative argument. ACM Trans. Math. Software 34 (4), pp. Art. 22, 21.

ⓘ

External Links:

ISSN 0098-3500, Document, MathReview Entry, ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

►

Algorithm 912: a module for calculating cylindrical functions of complex order and complex argument. ACM Trans. Math. Software 37 (4), pp. Art. 47, 25.

ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

2nd item, §10.77(viii).

Encodings:

BibTeX

… ►

The efficient evaluation of the hypergeometric function of a matrix argument. Math. Comp. 75 (254), pp. 833–846.

ⓘ

Notes:

For Matlab software for this function, see Plamen Koev’s home page.

External Links:

Home Page, ISSN 0025-5718, Document, MathReview (Luis Verde-Star), ZentralBlatt

Referenced by:

§35.10, 2nd item.

Encodings:

BibTeX

… ►

ZEBEC: A mathematical software package for computing simple zeros of Bessel functions of real order and complex argument. Comput. Phys. Comm. 113 (2-3), pp. 220–238.

ⓘ

Notes:

Double-precision Fortran, maximum accuracy 25S.

External Links:

ISSN 0010-4655, Document, Code, ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX

…

22: Bibliography L

… ►

Generating Bessel functions in Mie scattering calculations using continued fractions. Applied Optics 15 (3), pp. 668–671.

ⓘ

Referenced by:

§3.10(iii), §3.10(iii), Erratum (V1.0.24) for Paragraph Steed’s Algorithm (in §3.10(iii)).

Encodings:

BibTeX

… ►

Recurrence relations for hypergeometric functions of unit argument. Math. Comp. 45 (172), pp. 521–535.

ⓘ

External Links:

ISSN 0025-5718, FullText, MathReview (S. Conde), ZentralBlatt

Referenced by:

§16.4(iii).

Encodings:

BibTeX

… ►

Computations of spheroidal harmonics with complex arguments: A review with an algorithm. Phys. Rev. E 58 (5), pp. 6792–6806.

ⓘ

Notes:

Mathematica package for eigenvalues and solutions of the spheroidal wave equations

External Links:

Code(SpheroidF), Document

Referenced by:

2nd item, 3rd item.

Encodings:

BibTeX

… ►

Continued Fractions with Applications. Studies in Computational Mathematics, North-Holland Publishing Co., Amsterdam.

ⓘ

External Links:

ISBN 0-444-89265-6, MathReview (Olav Njåstad), ZentralBlatt

Referenced by:

§1.12(ii), §1.12(iv), §1.12(v), §15.7, §18.13, §3.10(ii), §3.10(iii), §3.11(iv), §4.25, §4.39, §4.9(i), §4.9(ii), §5.10, §6.9, §7.18(v), §7.9.

Encodings:

BibTeX

… ►

Two index laws for fractional integrals and derivatives. J. Austral. Math. Soc. 14, pp. 385–410.

ⓘ

External Links:

Document, MathReview (C. Fox), ZentralBlatt

Referenced by:

§1.15(vi), §1.15(vii).

Encodings:

BibTeX

…

23: 10.74 Methods of Computation

… ►The power-series expansions given in §§10.2 and 10.8, together with the connection formulas of §10.4, can be used to compute the Bessel and Hankel functions when the argument $x$ or $z$ is sufficiently small in absolute value. … ►It should be noted, however, that there is a difficulty in evaluating the coefficients $A_k(\zeta )$, $B_k(\zeta )$, $C_k(\zeta )$, and $D_k(\zeta )$, from the explicit expressions (10.20.10)–(10.20.13) when $z$ is close to $1$ owing to severe cancellation. … ►A comprehensive and powerful approach is to integrate the differential equations (10.2.1) and (10.25.1) by direct numerical methods. … ►

§10.74(v) Continued Fractions

►For applications of the continued-fraction expansions (10.10.1), (10.10.2), (10.33.1), and (10.33.2) to the computation of Bessel functions and modified Bessel functions see Gargantini and Henrici (1967), Amos (1974), Gautschi and Slavik (1978), Tretter and Walster (1980), Thompson and Barnett (1986), and Cuyt et al. (2008). …

24: Bibliography O

… ►

Hyperasymptotic solutions of higher order linear differential equations with a singularity of rank one. Proc. Roy. Soc. London Ser. A 454, pp. 1–29.

ⓘ

External Links:

ISSN 1364-5021, Document, MathReview (Donald A. Lutz), ZentralBlatt

Referenced by:

§2.11(v), §2.7(ii).

Encodings:

BibTeX

… ►

Hyperasymptotics for nonlinear ODEs. I. A Riccati equation. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2060), pp. 2503–2520.

ⓘ

External Links:

ISSN 1364-5021, Document, MathReview, ZentralBlatt

Referenced by:

§2.11(v).

Encodings:

BibTeX

… ►

A class of integral identities with matrix argument. Duke Math. J. 26 (2), pp. 207–213.

ⓘ

External Links:

Document, MathReview (R. Bellman), ZentralBlatt

Referenced by:

§35.3(ii).

Encodings:

BibTeX

… ►

Second-order differential equations with fractional transition points. Trans. Amer. Math. Soc. 226, pp. 227–241.

ⓘ

External Links:

FullText, MathReview (Anthony Leung), ZentralBlatt

Referenced by:

§2.8(v).

Encodings:

BibTeX

… ►

Numerical evaluation of the dilogarithm of complex argument. Celestial Mech. Dynam. Astronom. 62 (1), pp. 93–98.

ⓘ

External Links:

ISSN 0923-2958, Document, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§25.18(i).

Encodings:

BibTeX

…

25: Bibliography

… ►

Tables of $\ln \mathrm{\Gamma }(z)$ for Complex Argument. Pergamon Press, New York.

ⓘ

External Links:

ZentralBlatt

Referenced by:

§5.22(iii).

Encodings:

BibTeX

… ►

A subroutine package for Bessel functions of a complex argument and nonnegative order. Technical Report Technical Report SAND85-1018, Sandia National Laboratories, Albuquerque, NM.

ⓘ

External Links:

FullText

Referenced by:

1st item, B. Döring (1966).

Encodings:

BibTeX

►

Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order. ACM Trans. Math. Software 12 (3), pp. 265–273.

ⓘ

Notes:

Single and double precision, maximum accuracy 18S.

External Links:

ISSN 0098-3500, Document, Remark #1. Remark #2. GAMS (module 644; package TOMS), MathReview Entry, ZentralBlatt

Referenced by:

1st item, 1st item, 2nd item, 1st item.

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

… ►

Recurrence relations, continued fractions, and orthogonal polynomials. Mem. Amer. Math. Soc. 49 (300), pp. iv+108.

ⓘ

External Links:

ISSN 0065-9266, MathReview (W. A. Al-Salam), ZentralBlatt

Referenced by:

§18.28(iv).

Encodings:

BibTeX

…

26: Errata

… ►

Originally the function $\chi$ was presented with argument given by a positive integer $n$. It has now been clarified to be valid for argument given by a positive real number $x$.

… ►

A number of changes were made with regard to fractional integrals and derivatives. In §1.15(vi) a reference to Miller and Ross (1993) was added, the fractional integral operator of order $\alpha$ was more precisely identified as the Riemann-Liouville fractional integral operator of order $\alpha$, and a paragraph was added below (1.15.50) to generalize (1.15.47). In §1.15(vii) the sentence defining the fractional derivative was clarified. In §2.6(iii) the identification of the Riemann-Liouville fractional integral operator was made consistent with §1.15(vi).

… ►

In §15.6, it was noted that (15.6.8) can be rewritten as a fractional integral.

… ►

A new Subsection Continued Fractions, has been added to cover computation of confluent hypergeometric functions by continued fractions.

… ►

A new Subsection Continued Fractions, has been added to cover computation of the Gauss hypergeometric functions by continued fractions.

…