Some New Integral Representations of Generalized Mathieu Series and Alternating Mathieu Series

Zivorad Tomovski

Mathieu series ； alternating Mathieu series ； integral representations ； Laplace transform

Tamkang Journal of Mathematics

41卷4期（2010 / 12 / 01）

303 - 312

英文

The main purpose of this paper is to present a number of new integral representations for the familiar Mathieu series S(superscript α, β subscript μ), (r;{α(subscript k)}(superscript ∞ subscript k=1))(r ∈ R, α, β μ, {α(subscript k)}(superscript ∞ subscript k=1) ∈ R(superscript +) [12] as well as for its alternating version [8, 16] whenα(subscript k)=k(superscript p)=(superscript ∞ subscript k=1), α(subscript k)={(k!)(superscript p)}(superscript ∞ subscript k=1), α(subscript k)={(ln k!)(superscript p)}(superscript ∞ subscript k=1) with p=γ, γ(μα-β)＞1 and p=q/α, μ-β/α＞q^(-1), q∈N.