The transformation which assigns to a linear operator L the recurrence satis ed by coe cient se quences of the polynomial series in its kernel is shown to be an isomorphism of the corresponding operator algebras We use this fact to help factoring q di erence and recurrence operators and to nd nice power series solutions of linear di erential equations In particular we characterize generalized h...

Abstract A new family of p -Bernoulli numbers and polynomials was introduced by Rahmani (J. Number Theory 157:350–366, 2015) with the help Gauss hypergeometric function. Motivated that paper in light recent interests finding degenerate versions, we construct generalized Bernoulli means In addition, type Eulerian as a version numbers. For numbers, express them terms Stirling second kind, -Stirli...

We introduce generalized hypergeometric Bernoulli numbers for Dirichlet characters. study their properties, including relations, expressions and determinants. At the end in Appendix we derive first few of these numbers.

An integral representation is found for hypergeometric coherent states. It contains a generalized function. asymptotic expansion of states near z=1 constructed. This used to find eigenfunctions the Hamiltonian hydrogen atom in magnetic field lower boundaries spectral clusters.