Some results on the beta function and the incomplete beta function

Mongkolsery Lin; Brian Fisher; Somsak Orankitjaroen

doi:10.1142/S1793557115500485

Some results on the beta function and the incomplete beta function

Mongkolsery Lin
, Brian Fisher
, Somsak Orankitjaroen

Mahidol University
Universiry of Leicester

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

1 Citation (Scopus)

Abstract

The incomplete Beta function B(a,b; x) is defined for a,b > 0 and 0 < x < 1. This definition was extended to negative integer values of a and b by Özç et al. using neutrix limits. Partial derivatives of the incomplete Beta function B(a,b; x) for negative integer values of a and b were then evaluated. In the following, a number of results are obtained for the incomplete Beta function B(a,b; x) and then the corresponding results for the Beta function B(a,b) are deduced.

Original language	English
Article number	1550048
Journal	Asian-European Journal of Mathematics
Volume	8
Issue number	3
DOIs	https://doi.org/10.1142/S1793557115500485
Publication status	Published - 1 Sept 2015
Externally published	Yes

Keywords

Beta function
incomplete beta function
neutrix
neutrix limit

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10.1142/S1793557115500485

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title = "Some results on the beta function and the incomplete beta function",

abstract = "The incomplete Beta function B(a,b; x) is defined for a,b > 0 and 0 < x < 1. This definition was extended to negative integer values of a and b by {\"O}z{\c c} et al. using neutrix limits. Partial derivatives of the incomplete Beta function B(a,b; x) for negative integer values of a and b were then evaluated. In the following, a number of results are obtained for the incomplete Beta function B(a,b; x) and then the corresponding results for the Beta function B(a,b) are deduced.",

keywords = "Beta function, incomplete beta function, neutrix, neutrix limit",

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

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AU - Fisher, Brian

AU - Orankitjaroen, Somsak

PY - 2015/9/1

Y1 - 2015/9/1

N2 - The incomplete Beta function B(a,b; x) is defined for a,b > 0 and 0 < x < 1. This definition was extended to negative integer values of a and b by Özç et al. using neutrix limits. Partial derivatives of the incomplete Beta function B(a,b; x) for negative integer values of a and b were then evaluated. In the following, a number of results are obtained for the incomplete Beta function B(a,b; x) and then the corresponding results for the Beta function B(a,b) are deduced.

AB - The incomplete Beta function B(a,b; x) is defined for a,b > 0 and 0 < x < 1. This definition was extended to negative integer values of a and b by Özç et al. using neutrix limits. Partial derivatives of the incomplete Beta function B(a,b; x) for negative integer values of a and b were then evaluated. In the following, a number of results are obtained for the incomplete Beta function B(a,b; x) and then the corresponding results for the Beta function B(a,b) are deduced.

KW - Beta function

KW - incomplete beta function

KW - neutrix

KW - neutrix limit

UR - https://www.scopus.com/pages/publications/84951817204

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DO - 10.1142/S1793557115500485

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VL - 8

JO - Asian-European Journal of Mathematics

JF - Asian-European Journal of Mathematics

IS - 3

M1 - 1550048

ER -

Some results on the beta function and the incomplete beta function

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Keywords

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