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Title: | Representing the Stirling polynomials σn(x) in dependence of n and an application to polynomial zero identities | Authors: | Kovacec, Alexander Sá, Pedro Barata de Tovar |
Keywords: | Stirling polynomials; polynomial identities; difference equations; random flights; Riordan arrays | Issue Date: | 2023 | Publisher: | Walter de Gruyter | Project: | UID/ MAT/00324/2020 Gulbenkian Foundation - “Novos Talentos em Matemática” programme |
Serial title, monograph or event: | Special Matrices | Volume: | 11 | Issue: | 1 | Abstract: | Denote by σn the n-th Stirling polynomial in the sense of the well-known book Concrete Mathematics by Graham, Knuth and Patashnik. We show that there exist developments x σn (x) = σj = 0n (2jj!)-1 qn - j (j) xj with polynomials qj of degree j. We deduce from this the polynomial identities σ/a + b + c + d = n (-1)d (x - 2 a - 2 b)3n-s-a-c/a!b!c!d! (3n - s - a - c)! = 0, for s ϵ ℤ≥1, found in an attempt to find a simpler formula for the density function in a five-dimensional random flight problem. We point out a probable connection to Riordan arrays. | URI: | https://hdl.handle.net/10316/114831 | ISSN: | 2300-7451 | DOI: | 10.1515/spma-2022-0184 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais I&D CMUC - Artigos em Revistas Internacionais |
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