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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. https://doi.org/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. https://doi.org/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.
Keywords
factorials; binomial coefficients; combinatorial numbers; non-classical hypergeometric orthogonal polynomials; non-classical second-order hypergeometric linear DEs
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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