Name
Abstract | ||
|---|---|---|
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 J"@n(z) and the confluent hypergeometric functions "0F"1 and "1F"2 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. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1016/j.amc.2005.02.044 | Applied Mathematics and Computation |
Keywords | Field | DocType |
certain fredholm type,euler–maclaurin summation formula,weber–sonine integral,laplace integrals,dirichlet eta function,generalized mathieu series,mellin transforms,bernoulli numbers,riemann zeta function,landau bounds for j ν ( x ),mathieu a-series,fox–wright psi-functions,classical bessel function,asymptotic expansions,familiar mathieu a-series,bessel function of the first kind,mathieu and alternating mathieu a -series,bounding inequalities,integral representations,mathieu and alternating mathieu series,hypergeometric functions,mathieu type series,fourier transforms,dirichlet series,confluent hypergeometric function,special function,genocchi numbers,fredholm integral equation,integral equation,hypergeometric function,fourier transform,special functions,asymptotic expansion,bessel function,mellin transform,bernoulli number | Dirichlet eta function,Hypergeometric function,Riemann zeta function,Almost Mathieu operator,Dirichlet series,Mathematical analysis,Special functions,Bernoulli number,Mathematics,Mathieu function | Journal |
Volume | Issue | ISSN |
173 | 1 | Applied Mathematics and Computation |
Citations | PageRank | References |
7 | 3.09 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tibor Pogány | 1 | 32 | 13.73 |
| H. M. Srivastava | 2 | 179 | 43.20 |
| Ivorad Tomovski | 3 | 7 | 3.09 |