On defining the incomplete gamma function γ(-m, x-)

被引：9

作者：

Fisher, B ^{[1
]}

机构：

[1] Univ Leicester, Dept Math, Leicester LE1 7RH, Leics, England

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2004年 / 15卷 / 06期

关键词：

gamma function; incomplete Gamma function; Delta function;

D O I：

10.1080/10652460412331270698

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The incomplete Gamma function gamma(alpha, x_) is defined as a locally summable function on the real line for alpha > 0 by gamma (alpha, x_) = integral(0)(-x-) \u\(alpha-1) e(-u) du. the integral diverging alpha less than or equal to 0. The incomplete Gamma function gamma (alpha, x_) is then defined as a distribution for alpha < 0 and alpha not equal - 1, -2,... by using the recurrence formula gamma (alpha + 1.x_) = -alpha gamma(alpha, x_) - x_(alpha)e(-x). In the following, we define the distribution gamma (-m, x_) for m = 0, 1, 2.....

引用

页码：467 / 476

页数：10