Integral representation of a series which includes the Mathieu a-series
- Pogány, Tibor K
Publication date
August 2004
DOI Publisher
Elsevier Inc. ISSN
0022-247X Citation count (estimate)
19Abstract
AbstractIntegral expression is deduced for the series S(r,μ,ν,a)=∑n=1∞2F1ν−μ+12,ν−μ2+1;ν+1;−r2a(n)2a(n)ν−μ+1(a(n)2+r2)μ−1/2, where r>0, μ>1/2, ν+1<μ and a:0<a(1)<a(2)<⋯<a(n)↑∞, and 2F1 is the Gauß hypergeometric function. The result precizes the integral expression for the generalized Qi type Mathieu a-series S(r,p,a)=∑n=0∞a(n)(a(n)2+r2)−p−1 given in [J. Inequal. Pure Appl. Math. 4 (2003), (4.5)] generalizing some other results by Cerone and Lenard, Tomovski and Qi as well. Bounding inequalities are given for S(r,μ,ν,a) using the derived integral expression
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