New Computational Formulas for Special Numbers and Polynomials Derived from Applying Trigonometric Functions to Generating Functions

The aim of this paper is to apply trigonometric functions with functional equations of generating functions. Using the resulted new equations and formulas from this application, we obtain many special numbers and polynomials such as the Stirling numbers, Bernoulli and Euler type numbers, the array p...

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Bibliographic Details
Published in:Milan journal of mathematics 2021-06, Vol.89 (1), p.217-239
Main Authors: Kilar, Neslihan, Simsek, Yilmaz
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:The aim of this paper is to apply trigonometric functions with functional equations of generating functions. Using the resulted new equations and formulas from this application, we obtain many special numbers and polynomials such as the Stirling numbers, Bernoulli and Euler type numbers, the array polynomials, the Catalan numbers, and the central factorial numbers. We then introduce combinatorial sums related to these special numbers and polynomials. Moreover, we gave some remarks that relates our new findings from this paper to the relations found in earlier studies.
ISSN:1424-9286
1424-9294
DOI:10.1007/s00032-021-00333-y