Generalized incomplete gamma functions with applications

M. Aslam Chaudhry; S. M. Zubair

doi:10.1016/0377-0427(94)90187-2

Generalized incomplete gamma functions with applications

M. Aslam Chaudhry^*
, S. M. Zubair

^*Corresponding author for this work

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

226 Scopus citations

Abstract

In this paper, we introduce new functions as generalizations of the incomplete gamma functions. The functions are found to be useful in heat conduction, probability theory and in the study of Fourier and Laplace transforms. Some important properties of the functions are studied. We have investigated the asymptotic behavior, Laplace transforms, special cases, decomposition formula, integral representations, convolutions, recurrence relations and differentiation formula of these functions. Applications of these functions in evaluation of certain inverse Laplace transforms to the definite integrals and to the infinite series of exponential functions are shown.

Original language	English
Pages (from-to)	99-123
Number of pages	25
Journal	Journal of Computational and Applied Mathematics
Volume	55
Issue number	1
DOIs	https://doi.org/10.1016/0377-0427(94)90187-2
State	Published - 31 Oct 1994

Bibliographical note

Funding Information:
The authors acknowledge the support provided by the King Fahd University of Minerals. The useful commentsm ade by the referee are appreciated.

Keywords

Convolutions
Incomplete gamma functions
Laplace transforms

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/0377-0427(94)90187-2

Cite this

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title = "Generalized incomplete gamma functions with applications",

abstract = "In this paper, we introduce new functions as generalizations of the incomplete gamma functions. The functions are found to be useful in heat conduction, probability theory and in the study of Fourier and Laplace transforms. Some important properties of the functions are studied. We have investigated the asymptotic behavior, Laplace transforms, special cases, decomposition formula, integral representations, convolutions, recurrence relations and differentiation formula of these functions. Applications of these functions in evaluation of certain inverse Laplace transforms to the definite integrals and to the infinite series of exponential functions are shown.",

keywords = "Convolutions, Incomplete gamma functions, Laplace transforms",

author = "Chaudhry, \{M. Aslam\} and Zubair, \{S. M.\}",

note = "Funding Information: The authors acknowledge the support provided by the King Fahd University of Minerals. The useful commentsm ade by the referee are appreciated.",

year = "1994",

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T1 - Generalized incomplete gamma functions with applications

AU - Chaudhry, M. Aslam

AU - Zubair, S. M.

N1 - Funding Information: The authors acknowledge the support provided by the King Fahd University of Minerals. The useful commentsm ade by the referee are appreciated.

PY - 1994/10/31

Y1 - 1994/10/31

N2 - In this paper, we introduce new functions as generalizations of the incomplete gamma functions. The functions are found to be useful in heat conduction, probability theory and in the study of Fourier and Laplace transforms. Some important properties of the functions are studied. We have investigated the asymptotic behavior, Laplace transforms, special cases, decomposition formula, integral representations, convolutions, recurrence relations and differentiation formula of these functions. Applications of these functions in evaluation of certain inverse Laplace transforms to the definite integrals and to the infinite series of exponential functions are shown.

AB - In this paper, we introduce new functions as generalizations of the incomplete gamma functions. The functions are found to be useful in heat conduction, probability theory and in the study of Fourier and Laplace transforms. Some important properties of the functions are studied. We have investigated the asymptotic behavior, Laplace transforms, special cases, decomposition formula, integral representations, convolutions, recurrence relations and differentiation formula of these functions. Applications of these functions in evaluation of certain inverse Laplace transforms to the definite integrals and to the infinite series of exponential functions are shown.

KW - Convolutions

KW - Incomplete gamma functions

KW - Laplace transforms

UR - https://www.scopus.com/pages/publications/0002352357

U2 - 10.1016/0377-0427(94)90187-2

DO - 10.1016/0377-0427(94)90187-2

M3 - Article

AN - SCOPUS:0002352357

SN - 0377-0427

VL - 55

SP - 99

EP - 123

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

Generalized incomplete gamma functions with applications

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this