Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1047.33011
Kilbas, Anatoly A.; Saigo, Megumi; Saxena, R.K.
Generalized Mittag-Leffler function and generalized fractional calculus operators. (English)
[J] Integral Transforms Spec. Funct. 15, No. 1, 31-49 (2004). ISSN 1065-2469; ISSN 1476-8291/e

The paper studies the function $$E^\gamma_{\rho,\mu}(z)= \sum^\infty_{k=0} {(\gamma)_k\over \Gamma(\rho k+\mu)k!},$$ where $\rho$, $\mu$, and $\gamma$ are complex parameters with $\text{Re}(\rho)> 0$. This is a generalization of the classical Mittag-Leffler function $E_{\rho,\mu}(z)$ as well as a generalization of the Kummer confluent hypergeometric function $\Phi(\gamma,\mu,z)$.
[Kehe Zhu (Albany)]

MSC 2000:: *33E12 Mittag-Leffler functions and generalizations
33C15 Confluent hypergeometric functions
26A33 Fractional derivatives and integrals (real functions)
47B38 Operators on function spaces
47G10 Integral operators

Keywords: Mittag-Leffler function; hypergeometric function

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]