ORTHOGONALITY RELATIONS AND GENERATING-FUNCTIONS FOR JACOBI-POLYNOMIALS AND RELATED HYPERGEOMETRIC-FUNCTIONS

The authors begin by examining the validity of some orthogonality rela tions and expansion formulas (asserted recently by S. D. Bajpai [1]) i nvolving a class of hypergeometric polynomials which are essentially c ertain modified Jacobi polynomials. The corrected version of each of t hese orthogonality relations is shown to follow readily from the famil iar orthogonality property of the classical Jacobi polynomials. A brie f discussion is then presented about the applicability of an orthogona lity property for the first few Jacobi polynomials, but over a semi-in finite interval, which was considered by V. Romanovski [2] and (more r ecently) by S. D. Bajpai [3]. Several families of generating functions for Jacobi and Laguerre polynomials, and for various related hypergeo metric functions in one and more variables, are also considered system atically.