Sister Celine Fasenmyer's technique for obtaining pure recurrence relations for hypergeometric polynomials is formalized and generalized in various directions. Applications include algorithms for verifying any given binomial coefficients identity and any identities involving sums and integrals of products of special functions. This is shown to lead to a new approach to the theory of special functions which allows a natural definition of special functions of several variables.
All Science Journal Classification (ASJC) codes
- Applied Mathematics