The structural elucidation of Eisenstein’s formula
HASHIMOTO;Masahiro;KANEMITSU;Shigeru;;;;;;;;;;;;
【期刊名称】《中国科学》 【年(卷),期】2010(000)009
【摘要】In this paper,we shall give a complete structural description of generalizations of the classical Eisenstein formula that expresses the first periodic Bernoulli polynomial as a finite combination of cotangent values,as a relation between two bases of the vector space of periodic Dirichlet series.We shall also determine the limiting behavior of them,giving rise to Gauss’ famous closed formula for the values of the digamma function at rational points on the one hand and elucidation of Eisenstein-Wang’s formulas in the context of Kubert functions on the other.W shall reveal that most of the relevant previous results are the combinations of the generalized Eisenstein formula and the functional equation.
【总页数】10页(P.2341-2350) 【
关
键
词
】
Eisenstein;formula;Hurwitz;zeta-
function;polylogarithm;function;Gauss;formula
【作者】HASHIMOTO;Masahiro;KANEMITSU;Shigeru;;;;;;;;;;;;
【作者单位】of;Mathematics,Wakayama;College;of;Technology,Noda-machi;Gobo-shi;649-15,Japan;;School;of;Advanced;Technology,Kinki;University;Iizuka,Fukuoka
;820-8555,Japan; 【正文语种】英文 【中图分类】N 【相关文献】
1.Synthesis, structural characterization and properties of a 3D infinitely extended
structural
rare
earth
coordination
compound [J],
of
K3{[Sm(H2O)7]2Na[α-SiW11O39Sm(H2O)4]2}·14 Jingping; ZHAO; Junwei
H2O WANG;
2.Effect of Al Doping on Structural, Electrical, Optical and Photoluminescence Properties of Nano-Structural ZnO Thin Films [J], M. Mozibur Rahman; M.K.R. Khan; M. Rafiqul Islam; M.A. Halim; M. Shahjahan; M.A. Hakim; Dilip Kumar Saha; Jasim Uddin Khan
3.Structural Dimensions Analysis of Service Employees' Innovation Behavior Based on Structural Equation Model [J], LI Xia; DAI Chang-jun; ZHONG Jian-lan
4.Seeking Development in the Succession-An Analysis of Saussure's Structuralism and Strauss' Cultural Structuralism [J], 杨绍芳
5.Different effects of economic and structural performance indexes on model construction of structural topology optimization [J], G.L.Yi; Y.K.Sui
以上内容为文献基本信息，获取文献全文请下载
The structural elucidation of Eisenstein’s formula
