کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4637611 | 1340745 | 2006 | 40 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Some families of Mathieu a-series and alternating Mathieu a-series
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کلمات کلیدی
Genocchi numbersBernoulli numbers - اعداد برنولیFourier Transforms - تبدیل فوریهHypergeometric functions - توابع هیپرگومتریکDirichlet series - سری DirichletRiemann zeta function - عملکرد ریمان زتاEuler–Maclaurin summation formula - فرمول جمع بندی یولر مکلاورینFredholm integral equation - معادله انتگرالی FredholmMellin transforms - ملین تبدیل می شودIntegral representations - نمایندگی های یکپارچهAsymptotic expansions - گسترش انسجام
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Some families of Mathieu a-series and alternating Mathieu a-series Some families of Mathieu a-series and alternating Mathieu a-series](/preview/png/4637611.png)
چکیده انگلیسی
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 Riemann Zeta function and the Dirichlet Eta function are also considered. Such special functions as the classical Bessel function Jν(z) and the confluent hypergeometric functions 0F1 and 1F2 are characterized by means of certain Fredholm type integral equations of the first kind, which are associated with some of these Mathieu type series. Several integrals containing Mathieu type series are also evaluated. Finally, some closely-related new questions and open problems are indicated with a view to motivating further investigations on the subject of this paper.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 173, Issue 1, 1 February 2006, Pages 69-108
Journal: Applied Mathematics and Computation - Volume 173, Issue 1, 1 February 2006, Pages 69-108
نویسندگان
Tibor K. Pogány, H.M. Srivastava, Živorad Tomovski,