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.
Highlights
With coefficients f (n) (0) taken from the Taylor series of f ( x) in (1.1). This can be made by a linear integral transformation of the function f ( x) which is closely related to a Laplace transformation and which is called Sumudu transformation1
We consider fractional integration and differentiation (e.g., Bateman and Erdélyi [15], Vladimirov [16], Oldham and Spanier [17], Samko, Kilbas, Marichev [18]) which is often useful in connection with Sumudu transformation
It was shown that Sumudu transformation of a function f ( x) as a relative of Laplace transformation can lead to the evaluation of series by integral transformation of known series
Summary
It is not rare that we want to evaluate a new primarily unknown function f ( x) given by its power series of the following kind With coefficients f (n) (0) taken from the Taylor series of f ( x) in (1.1) This can be made by a linear integral transformation of the function f ( x) which is closely related to a Laplace transformation and which is called Sumudu transformation. This can be made by a linear integral transformation of the function f ( x) which is closely related to a Laplace transformation and which is called Sumudu transformation1 It was introduced by Watugala [1] and further developed by Belgacem and coauthors, e.g., [2] [3] [4] [5] [6] and many others, e.g., [7].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
