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- Title
Some Results on the Derivatives of the Gamma and Incomplete Gamma Function for Non-positive Integers.
- Authors
Zhongfeng Sun; Huizeng Qin
- Abstract
This paper is concerned with some recursive relations of the derivatives of the Gamma function Γ(a) and incomplete Gamma function Γ(a,z) for the complex value of. In particular, dnΓ/dan(-m)(n,m = 0,1,2...) can be expressed as linear forms in djΓ/daj(1)(j = 0,1,....n + 1) while ∂nΓ/∂an(-m,n) can be represented as the combination of ∂jΓ/∂aj(1,z)(j = 0,1,...,n+1) and the elementary functions. With the aid of these results, we can establish the closed forms of some special integrals associated with Γ(a) and Γ(a,z), which can be expressed by the Riemann zeta functions and some special constants.
- Subjects
GAMMA functions; RECURSIVE functions; INCOMPLETENESS theorems; DERIVATIVES (Mathematics); ZETA functions; INTEGERS
- Publication
IAENG International Journal of Applied Mathematics, 2017, Vol 47, Issue 3, p265
- ISSN
1992-9978
- Publication type
Article