On the asymptotic representation of the Euler gamma function by Ramanujan

被引：53

作者：

Karatsuba, EA ^{[1
]}

机构：

[1] RAS, Ctr Comp, Moscow 117967, Russia

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2001年 / 135卷 / 02期

关键词：

Euler gamma function; asymptotic representation; Stirling's formulas; uniform estimate of the remainder; monotonicity; Fourier series; Lagrange formula;

D O I：

10.1016/S0377-0427(00)00586-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The problem of approximation to the Euler gamma function on the basis of some Ramanujan's formulas is considered. The function h(x) = (g(x))(6) - (8x(3) + 4x(2) + x), where g(x) = (e/x)(x)Gamma (1 + x)/root pi, is, studied. It is proved that on the interval (1, infinity) the function h(x) is increasing monotonically from h(1) = 0.0111976... to h(infinity) = 1/30 = 0.0333... . (C) 2001 Published by Elsevier Science B.V.

引用

页码：225 / 240

页数：16

共 9 条

[1]

[Anonymous], CAN MATH SOC SER MON

[2]

Berndt B.C., 1999, J INDIAN MATH SOC, V236, P15

[3]

Karatsuba A. A., 1992, RIEMANN ZETA FUNCTIO, DOI [10.1515/9783110886146, DOI 10.1515/9783110886146]

[4] On the computation of the Euler constant γ [J].

Karatsuba, EA .

NUMERICAL ALGORITHMS, 2000, 24 (1-2) :83-97

[5]

KARATSUBA EA, 1999, 226 U HELS

[6]

KARATSUBA EA, 1999, 248 U HELS DEP MATH

[7]

Ramanujan S, 1988, The Lost Notebook and Other Unpublished Papers

[8]

WHITAKER ET, 1927, COURSE MODERN ANAL, V1

[9]

[No title captured]

← 1 →