Formulae bringing to light from certain classes of numbers and polynomials
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Date
2023
Journal Title
Journal ISSN
Volume Title
Publisher
Springer-Verlag Italia Srl
Access Rights
info:eu-repo/semantics/closedAccess
Abstract
With aid of generating functions and their functional equation methods and special functions involving trigonometric functions, the motivation of this paper is to study by blending certain families polynomials associated with the Bernoulli numbers and polynomials, the Euler numbers and polynomials, the Hermite type polynomials, the Stirling numbers, the telephone numbers, the Chebyshev polynomials. Therefore, the purpose of this paper is to examine certain families of numbers and functions related to generalized Hermite-Kampe de Feriet polynomials and trigonometric functions. By using functional equations of generating functions, we derive numerous new formulae and relations involving parametric Hermite type polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the generalized Hermite-Kampe de Feriet polynomials and the telephone numbers. Moreover, applying derivative operator to these generating functions, we give many recurrence relations and computational formulae, and certain finite sums. Finally, some special cases of these results are reduced to not only the well-known Chebyshev polynomials, which have applications in a wide variety of different areas, but also special trigonometric functions and finite sums.
Description
Keywords
Bernoulli numbers, Euler numbers, Hermite type polynomials, Stirling numbers, Telephone numbers, Chebyshev polynomials, Generating functions, Trigonometric functions
Journal or Series
Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas
WoS Q Value
Q1
Scopus Q Value
Q1
Volume
117
Issue
1
