It follows from Bateman [4] page 213 after setting = 1 2 . It can also be found with slight modi cation in Bateman [5] page122. However we are not aware of any reference where explicit formulas for the Fourier coef cients for Gegenbauer, Jacobi, Laguerre and Hermite polynomials can be found. In this article we use known formulas for the connection coef cients relating an arbitrary orthogonal po...

in this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

This research considers two traditional important questions, which are interesting, at least to most mathematicians. The first question arises in the theory of double sequences of complex numbers, which concerns the relationship, if any, between the following three limits of a double sequence s : N×N −→ C: 1. limn,m→∞ s(n, m), 2. limn→∞(limm→∞ s(n, m)), 3. limm→∞(limn→∞ s(n, m)). In particular,...

The solution of elliptic partial differential equations arises in 3D surface reconstruction and active contours. Most current approaches are iterative including finite element methods (FEM) and finite difference methods (FDM). In this paper, we describe a fast spectral method for solving elliptic equations over the unit sphere. A double Fourier series expansion is applied to model convex or sta...