Dual series equations involving heat polynomials

AbstractAn exact solution of dual series equations involving heat polynomials Pn,v (x, t) is given. Dual series equations involving generalized Laguerre polynomials considered by Lowndes, Srivastava, and Panda are shown to be special cases of the equations considered in the present paper. The solution derived here for the Laguerre case is different from those obtained by the previous authors. Values of the series on the intervals where these are not already specified are given. An exact solution of the associated dual sequence equations is also given. Certain integral and series representations for Pn,v (x, t) and Wn,v (x, t) are derived which are needed in the present analysis