Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

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

Highlights
Master Server