Integral representation of the four-parametric generalized Mittag-Leffler function

S. Rogosin; A. Koroleva

doi:10.1007/s10986-010-9090-4

Integral representation of the four-parametric generalized Mittag-Leffler function

S. Rogosin^*, A. Koroleva

^*Corresponding author for this work

Department of Physics

Belarusian State University

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

In this paper, we give a new integral representation of the four-parametric generalized Mittag-Leffler function introduced and studied by Djrbashian (Dzherbashian). The representation, obtained in this paper, contains an iterated integral, wherein the internal integral is a Cauchy-type integral, and the external one is a simple improper integral along the so-called Hankel path. The representation also contains the values of the special Wright functions.

Original language	English
Pages (from-to)	337-343
Number of pages	7
Journal	Lithuanian Mathematical Journal
Volume	50
Issue number	3
DOIs	https://doi.org/10.1007/s10986-010-9090-4
Publication status	Published - Jul 2010

Keywords

33E12
33C20
30E20
generalized Mittag-Leffler function
integral representation
asymptotics
Wright function

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title = "Integral representation of the four-parametric generalized Mittag-Leffler function",

abstract = "In this paper, we give a new integral representation of the four-parametric generalized Mittag-Leffler function introduced and studied by Djrbashian (Dzherbashian). The representation, obtained in this paper, contains an iterated integral, wherein the internal integral is a Cauchy-type integral, and the external one is a simple improper integral along the so-called Hankel path. The representation also contains the values of the special Wright functions.",

keywords = "33E12, 33C20, 30E20, generalized Mittag-Leffler function, integral representation, asymptotics, Wright function",

author = "S. Rogosin and A. Koroleva",

note = "Rogosin, S., Koroleva, A. (2010). Integral representation of the four-parametric generalized Mittag-Leffler function. Lithuanian Mathematical Journal, 50 (3), 337-343.",

year = "2010",

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doi = "10.1007/s10986-010-9090-4",

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T1 - Integral representation of the four-parametric generalized Mittag-Leffler function

AU - Rogosin, S.

AU - Koroleva, A.

N1 - Rogosin, S., Koroleva, A. (2010). Integral representation of the four-parametric generalized Mittag-Leffler function. Lithuanian Mathematical Journal, 50 (3), 337-343.

PY - 2010/7

Y1 - 2010/7

N2 - In this paper, we give a new integral representation of the four-parametric generalized Mittag-Leffler function introduced and studied by Djrbashian (Dzherbashian). The representation, obtained in this paper, contains an iterated integral, wherein the internal integral is a Cauchy-type integral, and the external one is a simple improper integral along the so-called Hankel path. The representation also contains the values of the special Wright functions.

AB - In this paper, we give a new integral representation of the four-parametric generalized Mittag-Leffler function introduced and studied by Djrbashian (Dzherbashian). The representation, obtained in this paper, contains an iterated integral, wherein the internal integral is a Cauchy-type integral, and the external one is a simple improper integral along the so-called Hankel path. The representation also contains the values of the special Wright functions.

KW - 33E12

KW - 33C20

KW - 30E20

KW - generalized Mittag-Leffler function

KW - integral representation

KW - asymptotics

KW - Wright function

UR - http://hdl.handle.net/2160/9313

U2 - 10.1007/s10986-010-9090-4

DO - 10.1007/s10986-010-9090-4

M3 - Article

SN - 0363-1672

VL - 50

SP - 337

EP - 343

JO - Lithuanian Mathematical Journal

JF - Lithuanian Mathematical Journal

IS - 3

ER -

Integral representation of the four-parametric generalized Mittag-Leffler function

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Keywords

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