Biomedical subjects
Publications and source records attributed to H M Srivastava.
An elegant expression is obtained for the product of the inverse Weierstrass-Laguerre transforms of two functions in terms of their convolution. It is also shown how the main result can be extended to hold for the product of the inverse Weierstrass-Laguerre transforms of several functions.
In an attempt to unify a number of generating functions for certain classes of generalized hypergeometric polynomials, Lagrange's expansion formula is applied to prove a generating relation for an n-dimensional polynomial with arbitrary coefficients. It is also shown how these coefficients can be specialized to obtain the generalized Lauricella function as a generating function for a class of generalized hypergeometric polynomials of several complex variables.
In the present paper, the author applies some of his earlier results which extend the well-known Hille-Hardy formula for the Laguerre polynomials to certain classes of generalized hypergeometric polynomials in order to derive various generalizations of a bilinear generating function for the Jacobi polynomials proved recently by Carlitz. The corresponding results for the polynomials of Legendre, Gegenbauer (or ultraspherical), Laguerre, etc., can be obtained fairly easily as the specialized or limiting cases of the generating functions presented here. It is also shown how the formula of Carlitz follows rather rapidly from a result of Weisner involving the Gaussian hypergeometric functions.