On type 2 degenerate Bernoulli and Euler polynomials of complex variable
| Autor: | Taekyun Kim, Dae San Kim, Lee-Chae Jang, Han-Young Kim |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Type 2 degenerate Bernoulli polynomials of complex variable
Type 2 degenerate Euler polynomials of complex variable Type 2 degenerate cosine-Bernoulli polynomials Type 2 degenerate sine-Bernoulli polynomials Type 2 degenerate cosine-Euler polynomials Type 2 degenerate sine-Euler polynomials Mathematics QA1-939 |
| Zdroj: | Advances in Difference Equations, Vol 2019, Iss 1, Pp 1-15 (2019) |
| Druh dokumentu: | article |
| ISSN: | 1687-1847 |
| DOI: | 10.1186/s13662-019-2419-3 |
| Popis: | Abstract Recently, Masjed-Jamei, Beyki, and Koepf studied the so-called new type Euler polynomials without using Euler polynomials of complex variable. Here we study the type 2 degenerate cosine-Euler and type 2 degenerate sine-Euler polynomials, which are type 2 degenerate versions of these new type Euler polynomials, by considering the degenerate Euler polynomials of complex variable and by treating the real and imaginary parts separately. In addition, we investigate the corresponding ones for Bernoulli polynomials in the same manner. We derive some explicit expressions for those new polynomials and some identities relating to them. Here we note that the idea of separating the real and imaginary parts separately gives an affirmative answer to the question asked by Hacène Belbachir. |
| Databáze: | Directory of Open Access Journals |
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