Formulas for special numbers and polynomials derived from functional equations of their generating functions

DOI10.55730/1300-0098.3280zbMath1495.05013OpenAlexW4285131101WikidataQ113689582 ScholiaQ113689582MaRDI QIDQ5102111

Neslihan Kilar

Publication date: 6 September 2022

Published in: Turkish Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.55730/1300-0098.3280

zbMATH Keywords

generating functionsFibonacci and Lucas numbersspecial numbers and polynomialsVieta polynomialsApostol type numbers and polynomialsparametric type polynomials

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bernoulli and Euler numbers and polynomials (11B68) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Real polynomials: analytic properties, etc. (26C05) Exponential and trigonometric functions (33B10)

Cites Work

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• Symbolic computation of some power-trigonometric series
• Generating functions for special polynomials and numbers including Apostol-type and Humbert-type polynomials
• Some new generalizations and applications of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials
• Identities and relations for Hermite-based Milne-Thomson polynomials associated with Fibonacci and Chebyshev polynomials
• A class of polynomials and connections with Bernoulli's numbers
• Fibonacci and Lucas Numbers With Applications
• Computational formulas and identities for new classes of Hermite‐based Milne–Thomson type polynomials: Analysis of generating functions with Euler's formula
• New families of special numbers for computing negative order Euler numbers and related numbers and polynomials
• A special approach to derive new formulas for some special numbers and polynomials
• Generating functions for two-variable polynomials related to a family of Fibonacci type polynomials and numbers

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