Some new integral representations of generalized Mathieu series and alternating Mathieu series
نویسندگان
چکیده
منابع مشابه
Some families of Mathieu a-series and alternating Mathieu a-series
The main purpose of this paper is to present a number of potentially useful integral representations for the familiar Mathieu a-series as well as for its alternating version. These results are derived here from many different considerations and are shown to yield sharp bounding inequalities involving the Mathieu and alternating Mathieu a-series. Relationships of the Mathieu a-series with the Ri...
متن کاملINTEGRAL REPRESENTATION OF MATHIEU (a,λ)-SERIES
In the article an integral representation of Mathieu (a,λ)-series S(%, p,a,λ) = ∑∞ n=0 a(n)(λ(n)+%) −p is obtained generalizing certain results by Guo, Tomovski, Tomovski and Trenčevski, and Qi. Bilateral bounding inequalities are given for S(%, p,a,λ) using this integral expression.
متن کاملOn Integral Forms of Generalised Mathieu Series
Integral representations for generalised Mathieu series are obtained which recapture the Mathieu series as a special case. Bounds are obtained through the use of the integral representations.
متن کاملAccurate Approximation of a Generalized Mathieu Series
New, accurate lower and upper bounds for the sum of the generalized Mathieu series ∞ ∑ k=1 2k (k2 + x2) , p > 0,
متن کاملNew upper bounds for Mathieu–type series
The Mathieu’s series S(r) was considered firstly by É.L. Mathieu in 1890; its alternating variant S̃(r) has been recently introduced by Pogány et al. [12] where various bounds have been established for S, S̃. In this note we obtain new upper bounds over S(r), S̃(r) with the help of Hardy–Hilbert double integral inequality. 2000 Mathematics Subject Classification. Primary: 26D15, 33E20.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Tamkang Journal of Mathematics
سال: 2010
ISSN: 2073-9826,0049-2930
DOI: 10.5556/j.tkjm.41.2010.772