Accurate approximations of the Mathieu series
نویسندگان
چکیده
منابع مشابه
Accurate 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,
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It is well known that the Mathieu series has a wide application in mathematics science. In this paper, we use the elementary method and construct some new inequalities to study the computational problem of the partial reciprocal sums related to the Mathieu series and obtain an interesting inequality and a related identity.
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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...
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 2011
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2010.10.027