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.
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页码：235 / 245
页数：11
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