The Glaisher rule is an operational identity involving the action of an exponential operator containing the second-order derivatives acting on an exponential function. We use the Crofton and monomiality formalism to derive generalized forms to the multi-dimensional case and show its usefulness in the derivation of old and new forms of generating functions for a wealth of Hermite polynomials families.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
Dattoli, G., Khan, S., & Ricci, P. E. (2008). On Crofton-Glaisher type relations and derivation of generating functions for Hermite polynomials including the multi-index case. Integral Transforms and Special Functions, 19(1), 1 - 9. https://doi.org/10.1080/10652460701358984