Generating functions and generalized Euler numbers

被引：12
|
作者：
Liu, Guodong [1 ]
机构：
[1] Huizhou Univ, Dept Math, Huizhou 516015, Guangdong, Peoples R China
来源：
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | 2008年 / 84卷 / 02期
关键词：
generating functions; the generalized Euler numbers; explicit formula; congruences;
D O I：
10.3792/pjaa.84.29
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we shall give an explicit formula for the coefficient of the expansion of a given generating function raised to an arbitrary power, when that function has an appropriate form. One of the many examples is the generalized Euler numbers and we shall clarify the situation surrounding the congruence Ep-1/2 not equivalent to 0(mod p), p equivalent to 1 (mod 4), a prime, and restore the priority. At the same time we shall state the true meaning of such a congruence.
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页码：29 / 34
页数：6
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