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Integral Representations of Generalized Mathieu Series Via Mittag-Leffler Type Functions

Tomovski, Živorad (2007)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 33C05, 33C10, 33C20, 33C60, 33E12, 33E20, 40A30The main purpose of this paper is to present a number of potentially useful integral representations for the generalized Mathieu series as well as for its alternating versions via Mittag-Leffler type functions.

Numeric-analytical construction of Mathieu functions

Yu. A. Ryabov (1999)

Mathematica Bohemica

In this paper we present an iterative algorithm for the construction of Mathieu functions of any order N in the form of Fourier series (practically, polynomials), and also the corresponding Quick-BASIC program for realization of this algorithm with numerical values of the parameter.

On the complex geometry of invariant domains in complexified symmetric spaces

Karl-Hermann Neeb (1999)

Annales de l'institut Fourier

Let M = G / H be a real symmetric space and 𝔤 = 𝔥 + 𝔮 the corresponding decomposition of the Lie algebra. To each open H -invariant domain D 𝔮 i 𝔮 consisting of real ad-diagonalizable elements, we associate a complex manifold Ξ ( D 𝔮 ) which is a curved analog of a tube domain with base D 𝔮 , and we have a natural action of G by holomorphic mappings. We show that Ξ ( D 𝔮 ) is a Stein manifold if and only if D 𝔮 is convex, that the envelope of holomorphy is schlicht and that G -invariant plurisubharmonic functions correspond to convex H -invariant...

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