Mittag-Leffler function

SearchAdvancedHelp

(0.001 seconds)

5 matching pages

1: 10.46 Generalized and Incomplete Bessel Functions; Mittag-Leffler Function

§10.46 Generalized and Incomplete Bessel Functions; Mittag-Leffler Function

… ►The Laplace transform of $\varphi (\rho ,\beta ;z)$ can be expressed in terms of the Mittag-Leffler function: ►

10.46.3 $$E_{a,b}\left(z\right)=\sum _{k=0}^{\mathrm{\infty }}\frac{z^k}{\mathrm{\Gamma }\left(ak+b\right)},$$ $a>0$.

ⓘ

Defines:

$E_{a,b}\left(z\right)$: Mittag-Leffler function

Symbols:

$\mathrm{\Gamma }\left(z\right)$: gamma function, $k$: nonnegative integer and $z$: complex variable

Permalink:

http://dlmf.nist.gov/10.46.E3

Encodings:

pMML, png, TeX

See also:

Annotations for §10.46 and Ch.10

… ►See also Wong and Zhao (2002a), and for further information on the Mittag-Leffler function see Erdélyi et al. (1955, §18.1), Paris and Kaminski (2001, §5.1.4), and Haubold et al. (2011). …

2: Bibliography P

… ►

Exponential asymptotics of the Mittag-Leffler function. Proc. Roy. Soc. London Ser. A 458, pp. 3041–3052.

ⓘ

External Links:

ISSN 1364-5021, Document, MathReview (Roderick Wong), ZentralBlatt

Referenced by:

§10.46.

Encodings:

BibTeX

…

3: Bibliography W

… ►

Exponential asymptotics of the Mittag-Leffler function. Constr. Approx. 18 (3), pp. 355–385.

ⓘ

External Links:

ISSN 0176-4276, Document, MathReview, ZentralBlatt

Referenced by:

§10.46.

Encodings:

BibTeX

…

4: Bibliography H

… ►

Mittag-Leffler functions and their applications. J. Appl. Math. 2011, pp. Art. ID 298628, 51 pages.

ⓘ

External Links:

ISSN 1110-757X, Document, FullText, MathReview (Rudolf Gorenflo), ZentralBlatt

Referenced by:

§10.46, §10.46.

Encodings:

BibTeX

…

5: 1.10 Functions of a Complex Variable

… ►

Analytic Functions

… ►

§1.10(vi) Multivalued Functions

… ►

§1.10(vii) Inverse Functions

… ►

Mittag-Leffler’s Expansion

… ►

§1.10(xi) Generating Functions

…