Result: Some consideration about Gegenbauer and Humbert polynomials

Title:
Some consideration about Gegenbauer and Humbert polynomials
Authors:
Milovanović, G. V., Marinković, S. D.
Publisher Information:
University of Niš, Faculty of Electronic Engineering, Department of Mathematics, Niš
Subject Terms:
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Elliptic integrals as hypergeometric functions, Gegenbauer polynomial, Humbert polynomials
Document Type:
Academic journal Article
File Description:
application/xml
Access URL:
https://zbmath.org/735354
Accession Number:
edsair.c2b0b933574d..c311d6446f11c8f29c3edb0dde369815
Database:
OpenAIRE

Further Information

Summary: Expanding the Gegenbauer polynomial \(C_ n^ \lambda (x)\) in powers of \(\lambda\), coefficients of that expansion are the polynomials \(g_{j,n} (x)\), \(j=1,\dots, n\). In this paper we give some explicit expressions for \(g_{j,n} (x)\), as well as a linear nonhomogeneous differential equation of the second order, satisfied by these polynomials. Also, we consider the similar problems for the Humbert polynomials \(p_{n,m}^ \lambda (x)\).