Year: 2018
Type: preprint
Abstract: In this paper, we obtain the analytical solutions of Laplace transforms based some novel integrals with suitable convergence conditions, by using hypergeometric approach (some algebraic properties of Pochhammer symbol and classical summation theorems of hypergeometric series ${}_{2}F_{1}(1)$, ${}_{2}F_{1}(-1)$ , ${}_{4}F_{3}(-1)$) . Also, we obtain the Laplace transforms of arbitrary powers of some finite series containing hyperbolic sine and cosine functions having different arguments, in terms of hypergeometric and Beta functions. Moreover, Laplace transforms of even and odd positive integral powers of sine and cosine functions with different arguments, and their combinations of the product (taking two, three, four functions at a time), are obtained. In addition, some special cases are yield from the main results.
Source: arXiv (Cornell University)
Authors: Qureshi, M. I., Dar, Showkat Ahmad
Institution: Jamia Millia Islamia
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2804328506