On Integral Forms of Generalised Mathieu Series

نویسنده

  • P. CERONE
چکیده

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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Integral expressions for Mathieu-type series whose terms contain Fox's H-function

Closed integral form expressions are derived for the Mathieu-type a-series and for the associated alternating series whose terms contain Fox’s H -function. In the final section, two similar results on Mathieu-type series with the Fox–Wright Psi-function pΨq and the generalized hypergeometric function pFq which can be expressed in terms of Fox’s H -functions are deduced respectively. c © 2006 El...

متن کامل

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 کامل

Generalized Ritt type and generalized Ritt weak type connected growth properties of entire functions represented by vector valued Dirichlet series

In this paper, we introduce the idea of generalized Ritt type and generalised Ritt weak type of entire functions represented by a vector valued Dirichlet series. Hence, we study some growth properties of two entire functions represented by a vector valued Dirichlet series on the basis of generalized Ritt type and generalised Ritt weak type.

متن کامل

INTEGRAL 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 کامل

Some Problems and Solutions Involving Mathieu’s Series and Its Generalizations

The authors investigate several recently posed problems involving the familiar Mathieu series and its various generalizations. For certain families of generalized Mathieu series, they derive a number of integral representations and investigate several one-sided inequalities which are obtainable from some of these general integral representations or from sundry other considerations. Relevant con...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003