ASYMPTOTIC EXPANSIONS OF INTEGRAL MEAN OF POLYGAMMA FUNCTIONS

被引：4

作者：

Chen, Chao-Ping ^{[1
]}

Elezovic, Neven ^{[2
]}

Vuksic, Lenka ^{[2
]}

机构：

[1] Henan Polytech Univ, Sch Math & Informat, Jiaozuo City 454003, Henan Province, Peoples R China

[2] Univ Zagreb, Fac Elect Engn & Comp, Zagreb 10000, Croatia

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2015年 / 18卷 / 01期

关键词：

Gamma function; psi function; polygamma functions; Bernoulli numbers and polynomials; asymptotic expansion; GAMMA-FUNCTION; INEQUALITIES; DIGAMMA; BOUNDS;

D O I：

10.7153/mia-18-19

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let s,t be two given real numbers, s not equal t and m is an element of N. We determine the coefficients a(j)(s,t) in the asymptotic expansion of integral (or differential) mean of polygamma functions Psi((m))(x) : 1/t - s integral(t)(s)Psi((m))(x + u) du similar to psi((m)) (x Sigma(infinity)(j=0) a(j)(s,t)/x(j)), x -> infinity. We derive the recursive relations for polynomials a(j)(t, s), and also as polynomials in intrinsic variables alpha = 1/2 (s + t - 1), beta = 1/4 [1 - (t - s)(2)]. We derive also the main properties of these polynomials and as a consequence the asymptotic formula for shifted variables.

引用

页码：255 / 266

页数：12

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