The Hurwitz zeta function as a convergent series

被引：4
作者：
Dwilewicz, Roman [1 ]
Minac, Jan
机构：
[1] Univ Missouri, Dept Math & Stat, Rolla, MO 65409 USA
[2] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland
[3] Univ Western Ontario, Dept Math, London, ON N6A 5B7, Canada
来源：
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2006年 / 36卷 / 04期
关键词：
Hurwitz zeta function; Bernoulli polynomials; Bernoulli numbers;
D O I：
10.1216/rmjm/1181069411
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
New series for the Hurwitz zeta function which converge on the whole plane, except s = 1, are developed. This is applied to obtain a remarkably simple evaluation of some special values of the function.
引用
收藏
页码：1191 / 1219
页数：29
相关论文
共 58 条
[21]   On some integrals involving the Hurwitz zeta function: Part 1 [J].
Espinosa, O ;
Moll, VH .
RAMANUJAN JOURNAL, 2002, 6 (02) :159-188
[22]   On some integrals involving the Hurwitz zeta function: Part 2 [J].
Espinosa, O ;
Moll, VH .
RAMANUJAN JOURNAL, 2002, 6 (04) :449-468
[23]   Pade approximants and equilibrated hypergeometric series [J].
Fischler, S ;
Rivoal, T .
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2003, 82 (10) :1369-1394
[24]  
Goncharov A. B., 1993, GELFAND MATH SEMINAR, P113
[25]   THE CLASSICAL TRILOGARITHM, ALGEBRAIC K-THEORY OF FIELDS, AND DEDEKIND ZETA-FUNCTIONS [J].
GONCHAROV, AB .
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 24 (01) :155-162
[26]   GEOMETRY OF CONFIGURATIONS, POLYLOGARITHMS, AND MOTIVIC COHOMOLOGY [J].
GONCHAROV, AB .
ADVANCES IN MATHEMATICS, 1995, 114 (02) :197-318
[27]  
Hardy G. H., 1949, Divergent Series
[28]  
Ireland K., 1990, GRAD TEXTS MATH, V84
[29]   Zeroes of zeta functions and symmetry [J].
Katz, NM ;
Sarnak, P .
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 36 (01) :1-26
[30]  
KATZ NM, 1999, AM MATH SOC COLL PUB, V45
123456