Displaying similar documents to “Summation of series by some substitutions”

Generalized analytic functions with applications to singular ordinary and partial differential equations

Bogdan Ziemian

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CONTENTS Introduction.............................................................................................................................................5 I. Preliminaries.........................................................................................................................................7    1. A review of classical results in the theory of Laplace integra............................................................7    2. Boundary values of holomorphic functions......................................................................................10...

On the Euler characteristic of the real Milnor fibres of an analytic function

Piotr Dudziński (2003)

Annales Polonici Mathematici

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The paper is concerned with the relations between real and complex topological invariants of germs of real-analytic functions. We give a formula for the Euler characteristic of the real Milnor fibres of a real-analytic germ in terms of the Milnor numbers of appropriate functions.

Laguerre polynomials in the inversion of Mellin transform

George J. Tsamasphyros, Pericles S. Theocaris (1981)

Aplikace matematiky

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In order to use the well known representation of the Mellin transform as a combination of two Laplace transforms, the inverse function g ( r ) is represented as an expansion of Laguerre polynomials with respect to the variable t = l n r . The Mellin transform of the series can be written as a Laurent series. Consequently, the coefficients of the numerical inversion procedure can be estimated. The discrete least squares approximation gives another determination of the coefficients of the series expansion....