Factorial series connected with the Lambert function, and a problem posed by Ramanujan

被引：9

作者：

Volkmer, Hans ^{[1
]}

机构：

[1] Univ Wisconsin, Dept Math Sci, Milwaukee, WI 53201 USA

来源：

RAMANUJAN JOURNAL | 2008年 / 16卷 / 03期

关键词：

Lambert function; Ramanujan's conjecture; factorial series; gamma function;

D O I：

10.1007/s11139-007-9104-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Ramanujan's sequence {y(n)}(n=0)(infinity) defined by Sigma(n-1)(j=0) n(j)/j ! + n(n)/n ! y(n) = e(n)/2 is expanded in factorial series derived from a series representing the Lambert W function. As a corollary, it is shown that the sequence {y(n)} is completely monotonic.

引用

页码：235 / 245

页数：11

共 50 条

[1] Factorial series connected with the Lambert function, and a problem posed by Ramanujan
Hans Volkmer
The Ramanujan Journal, 2008, 16 : 235 - 245
[2] LAMBERT SERIES AND RAMANUJAN
AGARWAL, RP
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 1993, 103 (03): : 269 - 293
[3] Fragments by Ramanujan on Lambert series
Berndt, BC
NUMBER THEORY AND ITS APPLICATIONS, 1999, 2 : 35 - 49
[4] ELEMENTARY PROOFS OF TWO THETA FUNCTION IDENTITIES OF RAMANUJAN AND CORRESPONDING LAMBERT SERIES IDENTITIES
Wang, Andrew Yezhou
COLLOQUIUM MATHEMATICUM, 2018, 152 (01) : 15 - 22
[5] ON MODULAR EQUATIONS AND LAMBERT SERIES FOR A CONTINUED FRACTION OF RAMANUJAN
Srivastava, Bhaskar
BULLETIN OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 3 (01): : 148 - 155
[6] ON A GENERALIZATION OF A RESULT OF RAMANUJAN CONNECTED WITH THE EXPONENTIAL SERIES
PARIS, RB
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1981, 24 (OCT) : 179 - 195
[7] A sharp version of Ramanujan’s inequality for the factorial function
Chao-Ping Chen
The Ramanujan Journal, 2016, 39 : 149 - 154
[8] A sharp version of Ramanujan's inequality for the factorial function
Chen, Chao-Ping
RAMANUJAN JOURNAL, 2016, 39 (01): : 149 - 154
[9] BAILEY CHAINS AND GENERALIZED LAMBERT SERIES .1. 4 IDENTITIES OF RAMANUJAN
ANDREWS, GE
ILLINOIS JOURNAL OF MATHEMATICS, 1992, 36 (02) : 251 - 274
[10] The Waring Problem with the Ramanujan τ-Function, II
Garaev, M. Z.
Garcia, V. C.
Konyagin, S. V.
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2009, 52 (02): : 195 - 199

← 1 2 3 4 5 →