Sumudu Transformation or What Else Can Laplace Transformation Do - Advances in Pure Mathematics

APM > Vol.9 No.2, February 2019

Sumudu Transformation or What Else Can Laplace Transformation Do ()

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DOI: 10.4236/apm.2019.92007 778 Downloads 1,572 Views

Author(s)

Alfred Wünsche

Affiliation(s)

Max-Planck-Group “Nonclassical Radiation” at Physical Institute of Humboldt University Berlin, Berlin, Germany.

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.

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

Share and Cite:

Wünsche, A. (2019) Sumudu Transformation or What Else Can Laplace Transformation Do. Advances in Pure Mathematics, 9, 111-142. doi: 10.4236/apm.2019.92007.

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