Application of a composition of generating functions for obtaining explicit formulas of polynomials

2012/11/01 by Kruchinin, Vladimir, Kruchinin, Dmitry
#05A15 #11B83 #11T06 #33D50 and etc #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1211.0099

Abstract

Using notions of composita and composition of generating functions we obtain explicit formulas for Chebyshev polynomials, Legendre polynomials, Gegenbauer polynomials, Associated Laguerre polynomials, Stirling polynomials, Abel polynomials, Bernoulli Polynomials of the Second Kind, Generalized Bernoulli polynomials, Euler Polynomials, Peters polynomials, Narumi polynomials, Humbert polynomials, Lerch polynomials and Mahler polynomials.

Related

• Composition of ordinary generating functions
• Composita and its properties
• New results on the associated Meixner, Charlier, Laguerre, and Krawtchouk polynomials
• Generalizations and specializations of generating functions for Jacobi,\n Gegenbauer, Chebyshev and Legendre polynomials with definite integrals
• Complementary Polynomials From Rodrigues' Representations For Confluent And Hypergeometric Functions And More