Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

New Concept of Factorials and Combinatorial Numbers and its Consequences for Algebra and Analysis

Version 1 : Received: 8 June 2021 / Approved: 9 June 2021 / Online: 9 June 2021 (07:39:47 CEST)

How to cite: Hassani, M.E. New Concept of Factorials and Combinatorial Numbers and its Consequences for Algebra and Analysis. Preprints 2021, 2021060243 (doi: 10.20944/preprints202106.0243.v1). Hassani, M.E. New Concept of Factorials and Combinatorial Numbers and its Consequences for Algebra and Analysis. Preprints 2021, 2021060243 (doi: 10.20944/preprints202106.0243.v1).

Abstract

In this article, the usual factorials and binomial coefficients have been generalized and extended to the negative integers. Basing on this generalization and extension, a new kind of polynomials has been proposed, which led directly to the non-classical hypergeometric orthogonal polynomials and the non-classical second-order hypergeometric linear DEs. The resulting polynomials can be used in non-relativistic and relativistic QM, particularly, in the case of the Schrödinger equation, and Dirac equations for an electron in a Coulomb potential field.

Subject Areas

factorials; binomial coefficients; combinatorial numbers; non-classical hypergeometric orthogonal polynomials; non-classical second-order hypergeometric linear DEs

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.