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
收藏
页码：298 / 314
页数：17
相关论文
共 50 条
[11]   On the Barnes double gamma function [J].
Alexanian, S. ;
Kuznetsov, A. .
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2023, 34 (12) :891-914
[12]   Simple error bounds for an asymptotic expansion of the partition function [J].
Nemes, Gergo .
RAMANUJAN JOURNAL, 2024, 65 (04) :1757-1771
[13]   Error bounds for the asymptotic expansion of the Hurwitz zeta function [J].
Nemes, G. .
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2017, 473 (2203)
[14]   ASYMPTOTIC EXPANSIONS FOR THE INCOMPLETE GAMMA FUNCTION IN THE TRANSITION REGIONS [J].
Nemes, Gergo ;
Daalhuis, Adri B. Olde .
MATHEMATICS OF COMPUTATION, 2019, 88 (318) :1805-1827
[15]   Asymptotic Expansion of the Modified Exponential Integral Involving the Mittag-Leffler Function [J].
Paris, Richard .
MATHEMATICS, 2020, 8 (03)
[16]   AN ASYMPTOTIC EXPANSION FOR THE FIRST DERIVATIVE OF THE HURWITZ-TYPE EULER ZETA FUNCTION [J].
Kim, Min-Soo .
JOURNAL OF APPLIED MATHEMATICS & INFORMATICS, 2023, 41 (06) :1409-1418
[17]   Error bounds and exponential improvement for the asymptotic expansion of the Barnes G-function [J].
Nemes, Gergo .
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2014, 470 (2172)
[18]   Asymptotic expansion of thick distributions [J].
Yang, Yunyun ;
Estrada, Ricardo .
ASYMPTOTIC ANALYSIS, 2015, 95 (1-2) :1-19
[19]   On the Coefficients of the Asymptotic Expansion of n! [J].
Nemes, Gergo .
JOURNAL OF INTEGER SEQUENCES, 2010, 13 (06)
[20]   On an asymptotic expansion in quantum theory [J].
Pechen, AN .
MATHEMATICAL NOTES, 2004, 75 (3-4) :426-429
12345