Five simultaneous fourier series equations

There has been a lot of work on dual, triple and quadruple series equations involving different polynomials. Due to the importance of these series equations in finding the solutions of various mixed boundary value problems of elasticity, electrostatics and other fields of mathematical physics, a number of researchers took interest in finding the series solution as well as developing and investigating new classes of series equations. There was almost no research work on five series equations until Dwivedi and Pandey taken it into consideration. They solved certain five series equations involving generalized Bateman K-functions, series of Jacobi and Laguerre and the product of ‘r’ generalized Bateman K-function. In the subsequent years Dwivedi and singh [5, 6], Dwivedi and Chandel [1], obtained the solution of five series equations involving generalized Bateman K-function and Jacobi polynomials respectively. In the present paper, we have considered five series equations involving series of Jacobi polynomials, which are extensions of quadruple series and untouched till date.