Some Extensions of the Mehler Formula

H. M. Srivastava, J. P. Singhal
1972 Proceedings of the American Mathematical Society  
By using certain operational techniques, the authors prove an elegant unification of several extensions of the well-known Mehler formula for Hermite polynomials, given recently by L. Carlitz ([1], [2] ). It is also shown how rapidly a number of Carlitz's formulas would follow from these considerations. The last section discusses a generalization involving the product of several Hermite polynomials of different arguments.
doi:10.2307/2038530 fatcat:y3cgdgluzrc6pcq3fidkjjiuam