LAUSR.org creates dashboard-style pages of related content for over 1.5 million academic articles. Sign Up to like articles & get recommendations!

On Generating Functions for Parametrically Generalized Polynomials Involving Combinatorial, Bernoulli and Euler Polynomials and Numbers

Photo from wikipedia

The aim of this paper is to give generating functions for parametrically generalized polynomials that are related to the combinatorial numbers, the Bernoulli polynomials and numbers, the Euler polynomials and… Click to show full abstract

The aim of this paper is to give generating functions for parametrically generalized polynomials that are related to the combinatorial numbers, the Bernoulli polynomials and numbers, the Euler polynomials and numbers, the cosine-Bernoulli polynomials, the sine-Bernoulli polynomials, the cosine-Euler polynomials, and the sine-Euler polynomials. We investigate some properties of these generating functions. By applying Euler’s formula to these generating functions, we derive many new and interesting formulas and relations related to these special polynomials and numbers mentioned as above. Some special cases of the results obtained in this article are examined. With this special case, detailed comments and comparisons with previously available results are also provided. Furthermore, we come up with open questions about interpolation functions for these polynomials. The main results of this paper highlight the existing symmetry between numbers and polynomials in a more general framework. These include Bernouilli, Euler, and Catalan polynomials.

Keywords: parametrically generalized; euler polynomials; functions parametrically; polynomials numbers; generating functions; euler

Journal Title: Symmetry
Year Published: 2022

Link to full text (if available)


Share on Social Media:                               Sign Up to like & get
recommendations!

Related content

More Information              News              Social Media              Video              Recommended



                Click one of the above tabs to view related content.