Some extensions of the Mehler formula
HTML articles powered by AMS MathViewer
- by H. M. Srivastava and J. P. Singhal PDF
- Proc. Amer. Math. Soc. 31 (1972), 135-141 Request permission
Abstract:
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.References
- Leonard Carlitz, An extension of Mehler’s formula, Boll. Un. Mat. Ital. (4) 3 (1970), 43–46 (English, with Italian summary). MR 0259204
- L. Carlitz, Some extensions of the Mehler formula, Collect. Math. 21 (1970), 117–130. MR 279354
- Earl D. Rainville, Special functions, The Macmillan Company, New York, 1960. MR 0107725
- J. P. Singhal, Certain extensions of the Mehler formula, Canad. Math. Bull. 15 (1972), 115–117. MR 315172, DOI 10.4153/CMB-1972-020-5
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 135-141
- DOI: https://doi.org/10.1090/S0002-9939-1972-0285738-4
- MathSciNet review: 0285738