NDLI: Outcomes of the Abel Identity

Content Provider	Springer Nature Link
Author	Petrullo, Pasquale
Copyright Year	2013
Abstract	We discuss some outcomes of an umbral generalization of the Abel identity. First we prove that a concise proof of the Lagrange inversion formula can be deduced from it. Second, we show that the whole class of Sheffer sequences, if manipulated to an umbral level, coincides with the subclass of Abel polynomials. Finally, we apply these techniques to obtain explicit formulae for some classical polynomial sequences, even in non Sheffer cases (Chebyshev and Gegenbauer polynomials).
Ending Page	1150
Page Count	10
Starting Page	1141
File Format	PDF
ISSN	16605446
e-ISSN	16605454
Journal	Mediterranean Journal of Mathematics
Issue Number	3
Volume Number	10
Language	English
Publisher	Springer Basel
Publisher Date	2013-02-27
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Lagrange inversion formula Power series rings Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) Umbral calculus Abel polynomials Mathematics Sheffer sequences Riordan arrays orthogonal polynomials
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Outcomes of the Abel Identity