JAC : A JOURNAL OF COMPOSITION THEORY ISSN : 0731-6755 GENERALIZED PROPERTIES ON MELLIN - WEIERSTRASS TRANSFORMS Amarnath Kumar Thakur Department of Mathematics Dr.C.V.Raman University, Bilaspur, State, Chhattisgarh Email-
[email protected] Gopi Sao Department of Mathematics Dr.C.V.Raman University, Bilaspur, State, Chhattisgarh Email-
[email protected] Hetram Suryavanshi Department of Mathematics Dr.C.V.Raman University, Bilaspur, State, Chhattisgarh Email-
[email protected] Abstract- In the present paper, we introduce definite integral transforms in operational calculus for the generalized properties on Mellin- Weierstrass associated transforms. These results are derived from the MW Properties These formulas may be considered as promising approaches in expressing in fractional calculus. Keywords – Laplace Transform , Convolution Transform Mellin Transforms , Weierstrass Transforms I. Introduction In mathematical terms the Fourier and Laplace transformations were introduced to solve physical problems. In fact, the first event of change is found by Reiman in which he used to study the famous zeta function. The Finnish mathematician Hjalmar Mellin (1854-1933), who was the first to give an orderly appearance change and its reversal,working in the theory of special functions, he developed applications towards a solution of hypergeometric differential equations and derivation of asymptotic expansions. Mellin's contribution gives a major place to the theory of analytic functions and essentially depends on the Cauchy theorem and the method of residuals. Actually, the Mellin transformation can also be placed in another framework, in which some cases is more closely related to Volume XIII, Issue IX, SEPTEMBER 2020 Page No: 98 JAC : A JOURNAL OF COMPOSITION THEORY ISSN : 0731-6755 original ideas of Reimann's original.In addition to its use in mathematics, Mellin's transformation has been applied in many different ways and areas of Physics and Engineering.