An asymptotic expansion of the double gamma function

被引：42

作者：

Ferreira, C ^{[1
]}

López, JL

机构：

[1] Univ Zaragoza, Fac Ciencias, Dept Math Aplicada, E-50013 Zaragoza, Spain

[2] Univ Publ Navarra, Dept Matemat & Informat, Pamplona 31006, Spain

来源：

JOURNAL OF APPROXIMATION THEORY | 2001年 / 111卷 / 02期

关键词：

Barnes double gamma function; asymptotic expansions;

D O I：

10.1006/jath.2001.3578

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Barnes double gamma function G(z) is considered for large argument z. A new integral representation is obtained for log G(z). An asymptotic expansion in decreasing powers of : and uniformly valid for \ Arg z \ < pi is derived from this integral. The expansion is accompanied by an error bound at any order of the approximation. Numerical experiments show that this bound is very accurate for real z. The accuracy of the error bound decreases for increasing Arg z. (C) 2001 Academic Press.

引用

页码：298 / 314

页数：17

共 50 条

[21] NEW ASYMPTOTIC EXPANSION AND ERROR BOUND FOR STIRLING FORMULA OF RECIPROCAL GAMMA FUNCTION
Pagola, Pedro J.
MATHEMATICAL INEQUALITIES & APPLICATIONS, 2018, 21 (04): : 957 - 965
[22] ERROR BOUNDS AND EXPONENTIAL IMPROVEMENT FOR HERMITE'S ASYMPTOTIC EXPANSION FOR THE GAMMA FUNCTION
Nemes, Gergo
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2013, 7 (01) : 161 - 179
[23] On the asymptotic expansion of a ratio of gamma functions
Laforgia, A.
Natalini, P.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 389 (02) : 833 - 837
[24] Asymptotic expansion of the period function
Saavedra, M
JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 193 (02) : 359 - 373
[25] Time asymptotic expansion of the tunneled wave function for a double-barrier potential
Petrillo, V
Olkhovsky, VS
EUROPHYSICS LETTERS, 2006, 74 (02): : 327 - 333
[26] ASYMPTOTIC EXPANSION OF DOUBLE FOURIER TRANSFORMS
DUFFIN, RJ
SHAFFER, DH
DUKE MATHEMATICAL JOURNAL, 1960, 27 (04) : 581 - 596
[27] Asymptotic expansions for the gamma function
Xu, Aimin
Hu, Yongcai
Tang, Peipei
JOURNAL OF NUMBER THEORY, 2016, 169 : 134 - 143
[28] A NOTE ON ASYMPTOTIC EXPANSION OF A RATIO OF GAMMA FUNCTIONS
FIELDS, JL
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1966, 15 : 43 - +
[29] Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function
Koumandos, Stamatis
Pedersen, Henrik L.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 355 (01) : 33 - 40
[30] ASYMPTOTIC-EXPANSION OF PERIOD FUNCTION
SAAVEDRA, M
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1994, 319 (06): : 563 - 566

← 1 2 3 4 5 →