On the approximation of a generalized incomplete gamma function arising in heat conduction problems

M. T. Boudjelkha; M. Aslam Chaudhry

doi:10.1006/jmaa.2000.6925

On the approximation of a generalized incomplete gamma function arising in heat conduction problems

M. T. Boudjelkha^*
, M. Aslam Chaudhry

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

4 Scopus citations

Abstract

Several asymptotic expansions are given for the generalized incomplete gamma function Γ(α,x;b)=∫^∞_xt^α-1e^-t-b/tdt, x0, Reb≥0, b≠0, as x tends to infinity, where the real parameter α is allowed to take negative values. In the case b=-iω, ω0, we obtain the expansions of the decomposition functions C_Γ(α,x;ω) and S_Γ(α,x;ω). Closed form expressions are also given for α=-3/2,-5/2,....

Original language	English
Pages (from-to)	509-519
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	248
Issue number	2
DOIs	https://doi.org/10.1006/jmaa.2000.6925
State	Published - 15 Aug 2000

Keywords

Generalized incomplete gamma function; decomposition functions; asymptotic expansion; error function; KdF function

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1006/jmaa.2000.6925

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title = "On the approximation of a generalized incomplete gamma function arising in heat conduction problems",

abstract = "Several asymptotic expansions are given for the generalized incomplete gamma function Γ(α,x;b)=∫∞xtα-1e-t-b/tdt, x0, Reb≥0, b≠0, as x tends to infinity, where the real parameter α is allowed to take negative values. In the case b=-iω, ω0, we obtain the expansions of the decomposition functions CΓ(α,x;ω) and SΓ(α,x;ω). Closed form expressions are also given for α=-3/2,-5/2,....",

keywords = "Generalized incomplete gamma function; decomposition functions; asymptotic expansion; error function; KdF function",

author = "Boudjelkha, \{M. T.\} and Chaudhry, \{M. Aslam\}",

year = "2000",

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AU - Boudjelkha, M. T.

AU - Chaudhry, M. Aslam

PY - 2000/8/15

Y1 - 2000/8/15

N2 - Several asymptotic expansions are given for the generalized incomplete gamma function Γ(α,x;b)=∫∞xtα-1e-t-b/tdt, x0, Reb≥0, b≠0, as x tends to infinity, where the real parameter α is allowed to take negative values. In the case b=-iω, ω0, we obtain the expansions of the decomposition functions CΓ(α,x;ω) and SΓ(α,x;ω). Closed form expressions are also given for α=-3/2,-5/2,....

AB - Several asymptotic expansions are given for the generalized incomplete gamma function Γ(α,x;b)=∫∞xtα-1e-t-b/tdt, x0, Reb≥0, b≠0, as x tends to infinity, where the real parameter α is allowed to take negative values. In the case b=-iω, ω0, we obtain the expansions of the decomposition functions CΓ(α,x;ω) and SΓ(α,x;ω). Closed form expressions are also given for α=-3/2,-5/2,....

KW - Generalized incomplete gamma function; decomposition functions; asymptotic expansion; error function; KdF function

UR - https://www.scopus.com/pages/publications/0034662553

U2 - 10.1006/jmaa.2000.6925

DO - 10.1006/jmaa.2000.6925

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SP - 509

EP - 519

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

On the approximation of a generalized incomplete gamma function arising in heat conduction problems

Abstract

Keywords

ASJC Scopus subject areas

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