The coefficients of differentiated expansions of double and triple Jacobi polynomials

Document Type : Research Paper


1 Cairo University-Faculty of Science-Mathematics Department

2 Helwan University-Faculty of Science-Mathematics Department


Formulae expressing explicitly the coefficients of an expansion of double Jacobi polynomials
which has been partially differentiated an arbitrary number of times with respect
to its variables in terms of the coefficients of the original expansion are stated and proved.
Extension to expansion of triple Jacobi polynomials is given. The results for the special
cases of double and triple ultraspherical polynomials are considered. Also the results
for Chebyshev polynomials of the first, second, third and fourth kinds and of Legendre
polynomials are noted. An application of how to use double Jacobi polynomials for
solving Poisson’s equation in two variables subject to nonhomogeneous mixed boundary
conditions is described.


Main Subjects