A Proof that extends hurwitz formula into the critical strip

M. T. Boudjelkha

doi:10.1016/S0893-9659(00)00168-3

A Proof that extends hurwitz formula into the critical strip

M. T. Boudjelkha^*

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

Abstract

Hurwitz formula for the generalized zeta function ζ(s,a) has been established under condition Re(s = σ < 0. Using the same contour integral, the proof proposed in this paper allows the extension of this formula into the critical strip, 0 < σ < 1. A similar result is obtained for the related function (1Γ(s)) ∫₀∞x^-s-1(e^-x)) dx, 0 < a ≤ 1.

Original language	English
Pages (from-to)	399-403
Number of pages	5
Journal	Applied Mathematics Letters
Volume	14
Issue number	4
DOIs	https://doi.org/10.1016/S0893-9659(00)00168-3
State	Published - May 2001

Keywords

Euler polynomials
Gamma function
Generalized zeta function
Hankel contour

ASJC Scopus subject areas

Applied Mathematics

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10.1016/S0893-9659(00)00168-3

Cite this

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title = "A Proof that extends hurwitz formula into the critical strip",

abstract = "Hurwitz formula for the generalized zeta function ζ(s,a) has been established under condition Re(s = σ < 0. Using the same contour integral, the proof proposed in this paper allows the extension of this formula into the critical strip, 0 < σ < 1. A similar result is obtained for the related function (1Γ(s)) ∫0∞x-s-1(e-x)) dx, 0 < a ≤ 1.",

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N2 - Hurwitz formula for the generalized zeta function ζ(s,a) has been established under condition Re(s = σ < 0. Using the same contour integral, the proof proposed in this paper allows the extension of this formula into the critical strip, 0 < σ < 1. A similar result is obtained for the related function (1Γ(s)) ∫0∞x-s-1(e-x)) dx, 0 < a ≤ 1.

AB - Hurwitz formula for the generalized zeta function ζ(s,a) has been established under condition Re(s = σ < 0. Using the same contour integral, the proof proposed in this paper allows the extension of this formula into the critical strip, 0 < σ < 1. A similar result is obtained for the related function (1Γ(s)) ∫0∞x-s-1(e-x)) dx, 0 < a ≤ 1.

KW - Euler polynomials

KW - Gamma function

KW - Generalized zeta function

KW - Hankel contour

UR - https://www.scopus.com/pages/publications/0035340944

U2 - 10.1016/S0893-9659(00)00168-3

DO - 10.1016/S0893-9659(00)00168-3

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AN - SCOPUS:0035340944

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SP - 399

EP - 403

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 4

ER -

A Proof that extends hurwitz formula into the critical strip

Abstract

Keywords

ASJC Scopus subject areas

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