On the incomplete gamma function and its neutrix convolution for negative integers

Mongkolsery Lin; Brian Fisher; Somsak Orankitjaroen

doi:10.32523/2077-9879-2019-10-1-30-51

On the incomplete gamma function and its neutrix convolution for negative integers

Mongkolsery Lin
, Brian Fisher
, Somsak Orankitjaroen

Institute of Technology of Cambodia
Universiry of Leicester
Mahidol University

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

1 Citation (Scopus)

Abstract

We define the distributions γ ⁺(-r, x) and γ ^-(-r, x) from the incomplete Gamma function γ (-r, x) for negative integers. We then evaluate some convolutions and neutrix convolutions of these distributions and the functions (x^s)+, (x^s)- and x^s.

Original language	English
Pages (from-to)	30-51
Number of pages	22
Journal	Eurasian Mathematical Journal
Volume	10
Issue number	1
DOIs	https://doi.org/10.32523/2077-9879-2019-10-1-30-51
Publication status	Published - 2019
Externally published	Yes

Keywords

Convolution
Gamma function
Incomplete Gamma function
Neutrix convolution

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10.32523/2077-9879-2019-10-1-30-51

Cite this

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title = "On the incomplete gamma function and its neutrix convolution for negative integers",

abstract = "We define the distributions γ +(-r, x) and γ -(-r, x) from the incomplete Gamma function γ (-r, x) for negative integers. We then evaluate some convolutions and neutrix convolutions of these distributions and the functions (xs)+, (xs)- and xs.",

keywords = "Convolution, Gamma function, Incomplete Gamma function, Neutrix convolution",

author = "Mongkolsery Lin and Brian Fisher and Somsak Orankitjaroen",

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T1 - On the incomplete gamma function and its neutrix convolution for negative integers

AU - Lin, Mongkolsery

AU - Fisher, Brian

AU - Orankitjaroen, Somsak

N1 - Publisher Copyright: © The Eurasian National University.

PY - 2019

Y1 - 2019

N2 - We define the distributions γ +(-r, x) and γ -(-r, x) from the incomplete Gamma function γ (-r, x) for negative integers. We then evaluate some convolutions and neutrix convolutions of these distributions and the functions (xs)+, (xs)- and xs.

AB - We define the distributions γ +(-r, x) and γ -(-r, x) from the incomplete Gamma function γ (-r, x) for negative integers. We then evaluate some convolutions and neutrix convolutions of these distributions and the functions (xs)+, (xs)- and xs.

KW - Convolution

KW - Gamma function

KW - Incomplete Gamma function

KW - Neutrix convolution

UR - https://www.scopus.com/pages/publications/85066235261

U2 - 10.32523/2077-9879-2019-10-1-30-51

DO - 10.32523/2077-9879-2019-10-1-30-51

M3 - Article

AN - SCOPUS:85066235261

SN - 2077-9879

VL - 10

SP - 30

EP - 51

JO - Eurasian Mathematical Journal

JF - Eurasian Mathematical Journal

IS - 1

ER -

On the incomplete gamma function and its neutrix convolution for negative integers

Abstract

Keywords

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