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

Mohamed Elmansour Hassani

doi:10.20944/preprints202106.0243.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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.

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

Computer Science and Mathematics, Algebra and Number Theory

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

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