Operator calculus approach to orthogonal polynomial expansions
The close relationship between Meixner polynomials and representations of Heisenberg algebra is used to obtain expressions for the generalized Fourier coefficients of a function expanded in a series of orthogonal polynomials of Meixner type. From these formulas, the authors show how to compute the coefficients using techniques of operational calculus. The particular case of Krawtchouk polynomials is discussed in detail and includes an algorithm for computing Krawtchouk transforms.
scientific article; zbMATH DE number 908321