Application of generalized M-series and H(bar)-function in electric circuit theory

Abstract

In this paper, we find the application and importance of certain
product of generalized M-series with H(bar)-function of general nature in the theory of electric circuit. The value of the charge at any time x in a simple electric circuit consisting of a electromotive force E P(x) 0 can be easily obtained for specific values of P(x). If P(x) is taken in terms of the product of generalized M-series and the H(bar)-function, the value of the charge thus obtained unifies the scattered results got by taking its values in terms of other simpler functions. This is an account of the fact that the generalized M-series and the H(bar)-function are one of the most general functions and almost all the important function occurring in physics and electrical engineering viz. Lorengzo-Hartlay R-function, reduced to Green function, generalized Riemann zeta function,
generalized Mittage-Leffler function etc. are its particular cases. Moreover, the product of the generalized M-series and the H(bar)-function is expressible in terms of Fourier series, hence even if P(x) is given in terms of Fourier series, we can obtain the value of the charge.