Heine%20integral

SearchAdvancedHelp

(0.003 seconds)

1—10 of 475 matching pages

1: 1.14 Integral Transforms

§1.14 Integral Transforms

… ►where the last integral denotes the Cauchy principal value (1.4.25). … ►If $f(t)$ is absolutely integrable on $[0,R]$ for every finite $R$, and the integral (1.14.47) converges, then … ►

§1.14(viii) Compendia

►For more extensive tables of the integral transforms of this section and tables of other integral transforms, see Erdélyi et al. (1954a, b), Gradshteyn and Ryzhik (2000), Marichev (1983), Oberhettinger (1972, 1974, 1990), Oberhettinger and Badii (1973), Oberhettinger and Higgins (1961), Prudnikov et al. (1986a, b, 1990, 1992a, 1992b).

2: 8.19 Generalized Exponential Integral

§8.19 Generalized Exponential Integral

►

§8.19(i) Definition and Integral Representations

… ►

Other Integral Representations

… ►

§8.19(ii) Graphics

… ►

§8.19(x) Integrals

…

3: 6.2 Definitions and Interrelations

… ►

§6.2(i) Exponential and Logarithmic Integrals

… ► … ►The logarithmic integral is defined by … ►

§6.2(ii) Sine and Cosine Integrals

… ► …

4: 8.21 Generalized Sine and Cosine Integrals

§8.21 Generalized Sine and Cosine Integrals

… ►

§8.21(iii) Integral Representations

… ►

§8.21(iv) Interrelations

… ►

§8.21(v) Special Values

… ►

5: 7.2 Definitions

… ►

§7.2(ii) Dawson’s Integral

… ►

§7.2(iii) Fresnel Integrals

… ►

Values at Infinity

… ►

§7.2(iv) Auxiliary Functions

… ►

§7.2(v) Goodwin–Staton Integral

…

6: 7.18 Repeated Integrals of the Complementary Error Function

§7.18 Repeated Integrals of the Complementary Error Function

►

§7.18(i) Definition

… ►

§7.18(iii) Properties

… ► … ►

Hermite Polynomials

…

7: 19.16 Definitions

… ►

§19.16(i) Symmetric Integrals

… ► … ►All other elliptic cases are integrals of the second kind. …(Note that $R_C(x,y)$ is not an elliptic integral.) … ►Each of the four complete integrals (19.16.20)–(19.16.23) can be integrated to recover the incomplete integral: …

8: 36.2 Catastrophes and Canonical Integrals

§36.2 Catastrophes and Canonical Integrals

►

§36.2(i) Definitions

… ►

Canonical Integrals

… ► … ►

§36.2(iii) Symmetries

…

9: 19.2 Definitions

… ►

§19.2(i) General Elliptic Integrals

… ►is called an elliptic integral. … ►

§19.2(ii) Legendre’s Integrals

… ►

§19.2(iii) Bulirsch’s Integrals

… ►

§19.2(iv) A Related Function: $R_C(x,y)$

…

10: Bibliography V

… ►

An integral transform involving Heun functions and a related eigenvalue problem. SIAM J. Math. Anal. 17 (3), pp. 688–703.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (William L. Perry), ZentralBlatt

Referenced by:

§31.10(i).

Encodings:

BibTeX

… ►

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

… ►

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

ⓘ

External Links:

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

Referenced by:

§31.15(iii).

Encodings:

BibTeX

… ►

Integral relations for Lamé functions. SIAM J. Math. Anal. 13 (6), pp. 978–987.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (F. M. Arscott), ZentralBlatt

Referenced by:

§29.8, §29.8.

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

…