Result: Some integral and asymptotic formulas associated with the Hurwitz Zeta function: Some integral and asymptotic formulas associated with the Hurwitz zeta function
Title:
Some integral and asymptotic formulas associated with the Hurwitz Zeta function: Some integral and asymptotic formulas associated with the Hurwitz zeta function
Source:
Applied Mathematics and Computation. 154:641-664
Publisher Information:
Elsevier BV, 2004.
Publication Year:
2004
Subject Terms:
Zeta-functions, Confluent hypergeometric function, Bernoulli polynomials, Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals), Euler-Maclaurin summation formula, Hurwitz and Lerch zeta functions, 01 natural sciences, Incomplete gamma function, Euler-Maclaurin formula in numerical analysis, Explicit formulas, Generalized Euler constants, Digamma function, Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\), 0101 mathematics, Bernoulli and Euler numbers and polynomials, Generalized Stirling formula
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
0096-3003
DOI:
10.1016/s0096-3003(03)00740-9
Access URL:
Rights:
Elsevier TDM
Accession Number:
edsair.doi.dedup.....dbdc8065cf9fd4d7f2a5e93b00d3af0b
Database:
OpenAIRE
Further Information
The main object of this paper is to present an integral representation of the partial sum \(L_u(x, a)=\sum_{0\leq n\leq x}(n+a)^u\) of the Hurwitz zeta function \(\zeta(-u, a)\), which entails a number of implications for \(L_u(x, a)\) and \(\zeta(-u, a)\) and for their derivatives.