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- Title
Representation of Multiple Integrals via the Generalized Lerch Transcendent.
- Authors
Zhongfeng Sun; Aijuan Li; Huizeng Qin
- Abstract
In this paper, we derive several properties of the generalized Lerch transcendent Φ(z, ..., ...) and the generalized Euler sum with parameters H(z, ..., ...), and establish their connections with some certain types of multiple integrals. In particular, Φ(z, ..., ...) and H(z, ..., ...) can be expressed as the linear combination of the Lerch transcendent Φ(z, s, u) and the Euler sum with parameters H(z, s, u), respectively. With the aid of those connections, the closed forms of some special multiple integrals which can be expressed by the special constants and the Riemann zeta functions are established.
- Subjects
MULTIPLE integrals; MATHEMATICAL notation; ZETA functions; DERIVATIVES (Mathematics); RIEMANN-Hilbert problems
- Publication
IAENG International Journal of Applied Mathematics, 2016, Vol 46, Issue 4, p412
- ISSN
1992-9978
- Publication type
Article