TITLE:
Sumudu Transformation or What Else Can Laplace Transformation Do
AUTHORS:
Alfred Wünsche
KEYWORDS:
Mellin Transformation, Fractional Integration, Geometric Series and Exponential Series, Error Function, Laguerre Polynomials, Generating Functions of Hermite Polynomials, Bessel Functions, Asymptotic Series, Operator Identities
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.9 No.2,
February
26,
2019
ABSTRACT: The transition from a known Taylor series of a known function f(x) to a new function primarily defined by
the infinite power series with coefficients f(n)(0)from the Taylor series
of the function f(x)can be made by an
integral transformation which is a modified Laplace transformation and is
called Sumudu transformation. It makes the transition from the Exponential
series to the Geometric series and may help to evaluate new infinite power
series from known Taylor series. The Sumudu transformation is
demonstrated to be a limiting case of Fractional integration. Apart from the
basic Sumudu integral transformation we discuss a modification where the
coefficients from the Taylor series
are not changed to f(n)(0)but only to . Beside simple examples our applications are mainly
concerned to calculate new Generating functions for Hermite polynomials from
the basic ones.