Remarks on combinatorial sums associated with special numbers and polynomials with their generating functions
Remarks on combinatorial sums associated with special numbers and polynomials
Keywords:Bernoulli numbers and polynomials, Euler numbers and polynomials, Stirling numbers, Daehee numbers, Changhee numbers, Parametrically generalized polynomials, Generating functions, Special functions, Special numbers and polynomials
The purpose of this article is to give some novel identities and inequalities associated with combinatorial sums involving special numbers and polynomials. In particular, by using the method of generating functions and their functional equations, we derive not only inequalities, but also some other formulas, identities, and relations for the parametrically generalized polynomials and for other known special numbers and polynomials. Our identities, relations, inequalities and combinatorial sums are related to the Bernoulli numbers and polynomials of negative order, the Euler numbers and polynomials of negative order, the Stirling numbers, the Daehee numbers, the Changhee numbers, the Bernoulli polynomials, the Euler polynomials, the parametrically generalized polynomials, and other well-known special numbers and polynomials. Moreover, using Mathematica with the help of the Wolfram programming language, we illustrate some plots of the parametrically generalized polynomials under some of their randomly selected special conditions. Finally, we give some remarks and observations on our results.
How to Cite
The copyright to the article is transferred to body International Journal of Maps in Mathematics effective if and when the article is accepted for publication.
- The copyright transfer covers the exclusive right to reproduce and distribute the article, including reprints, translations, photographic reproductions, microform, electronic form (offline, online) or any other reproductions of similar nature.
- An author may make his/her article published by body International Journal of Maps in Mathematics available on his/her home page provided the source of the published article is cited and body International Journal of Maps in Mathematics is mentioned as copyright owner.
- The author warrants that this contribution is original and that he/she has full power to make this grant. The author signs for and accepts responsibility for releasing this material on behalf of any and all co-authors. After submission of this agreement signed by the corresponding author, changes of authorship or in the order of the authors listed will not be accepted by body International Journal of Maps in Mathematics.