A special approach to derive new formulas for some special numbers and polynomials

DOI10.3906/mat-2005-116zbMath1493.05019OpenAlexW3100046681MaRDI QIDQ5099821

Neslihan Kilar, Yilmaz Simsek

Publication date: 26 August 2022

Published in: TURKISH JOURNAL OF MATHEMATICS (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3906/mat-2005-116

zbMATH Keywords

generating functionsChebyshev polynomialstrigonometric functionsLaplace operatorharmonic functionsFibonacci and Lucas polynomialsBernoulli and Euler type numbers and polynomials

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bernoulli and Euler numbers and polynomials (11B68) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Harmonic functions on Riemann surfaces (30F15) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Real polynomials: analytic properties, etc. (26C05) Exponential and trigonometric functions (33B10)

Related Items (5)

Formulas for special numbers and polynomials derived from functional equations of their generating functions ⋮ Formulae bringing to light from certain classes of numbers and polynomials ⋮ Recurrence relations, associated formulas, and combinatorial sums for some parametrically generalized polynomials arising from an analysis of the Laplace transform and generating functions ⋮ Identities and relations for Hermite-based Milne-Thomson polynomials associated with Fibonacci and Chebyshev polynomials ⋮ New computational formulas for special numbers and polynomials derived from applying trigonometric functions to generating functions

Cites Work

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• Some new identities and inequalities for Bernoulli polynomials and numbers of higher order related to the Stirling and Catalan numbers
• Incomplete generalized Jacobsthal and Jacobsthal-Lucas numbers
• Combinatorial trigonometry with Chebyshev polynomials
• Generating functions for special polynomials and numbers including Apostol-type and Humbert-type polynomials
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• Wirtinger type inequalities for higher order differentiable functions
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