Integral Representations of Functional Series with Members Containing Jacobi Polynomials

MSC 2010: Primary 33C45, 40A30; Secondary 26D07, 40C10In this article we establish a double definite integral representation, and two other indefinite integral expressions for a functional series and its derivative with members containing Jacobi polynomials

Integral expressions for Hilbert-type infinite multilinear form and related multiple Hurwitz-Lerch Zeta functions

The article deals with different kinds integral expressions concerning multiple Hurwitz-Lerch Zeta function (introduced originally by Barnes ), Hilbert-type infinite multilinear form and its power series extension. Here Laplace integral forms and multiple Mellin-Barnes type integral representation are derived for these special functions. As a special cases of our investigations we deduce the integral expressions for the Matsumoto's multiple Mordell-Tornheim Zeta function, that is, for Tornheim's double sum i.e. Mordell-Witten Zeta, for the multiple Hurwitz Zeta and for the multiple Hurwitz-Euler Eta function, recently studied by Choi and Srivastava

On the multidimensional sampling theorem

The well known sampling theorem is extended to the multidimensional weakly stationary (but not necessarily band-limited) processes. The mean square and almost sure convergence of the sampling expansion sum is derived for full spectrum multidimensional processes

Univalence criteria for linear fractional differential operators associated with a generalized Bessel function

In this paper our aim is to establish some generalizations upon the sufficient conditions for linear fractional differential operators involving the normalized forms of the generalized Bessel functions of the first kind to be univalent in the open unit disk as investigated recently by [{sc E. Deniz, H. Orhan, H.M. Srivastava}, {it Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions}, Taiwanese J. Math. {bf 15} (2011), No. 2, 883-917] and [{sc \u27A. Baricz, B. Frasin}, {it Univalence of integral operators involving Bessel functions}, Appl. Math. Letters {bf 23} (2010), No. 4, 371--376]. Our method uses certain Luke\u27s bounding inequalities for hypergeometric functions ${}_{p+1}F_p$ and ${}_pF_p$

Second Type Neumann Series Related to Nicholson’s and to Dixon–Ferrar Formula

The second type Neumann series are considered which building blocks are Nicholson’s and the Dixon–Ferrar formulae for (Formula Presented). Related closed form double definite integral expressions are established by using the associated Dirichlet’s series Cahen’s Laplace integral for the Nicholson’s case. However, using Dixon–Ferrar formula a double definite integral expression is again obtained. Certain Open Problems are posed in the last section of the chapter

Solstice: An Electronic Journal of Geography and Mathematics, Volume XXIII, Number 2

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