A Formal Solution of Quadruple Series Equations

Abstract

It cannot be overstated how significant Series Equations are to the fields of pure and applied mathematics respectively. The majority of mathematical topics revolve around the use of series. Virtually, in every subject of mathematics, series play an important role. Series solutions play a major role in the solution of mixed boundary value problems. Dual, triple, and quadruple series equations are useful in finding the solution of four part boundary value problems of electrostatics, elasticity and other fields of Mathematical physics. Cooke devised a method for finding the solution of quadruple series equations involving Fourier-Bessel series and obtained the solution using operator theory. Several workers have devoted considerable attention to the solutions of various equations involving for instance, trigonometric series, The Fourier-Bessel series, The Fourier Legendre series, The Dini series, series of Jacobi and Laguerre polynomials and series equations involving Bateman K-functions. Indeed, many of these problems arise in the investigation of certain classes of mixed boundary value problems in potential theory. There has been less work on quadruple series equations involving various polynomials and functions. In light of the significance of quadruple series solutions, proposed work examines quadruple series equations that include the product of r generalised Bateman K functions. Solution is formal, and there has been no attempt made to rationalise many restricting processes that have been encountered.