On an analogue of Euler polynomials and related to extended fermionic \(p\)-adic integrals on \( \mathbb{Z}_{p} \). (English) Zbl 1391.11039
Summary: In the paper, using the extended fermionic \(p\)-adic integral on \( \mathbb{Z}_{p} \), the authors find some applications of the umbral calculus. From these applications, the authors derive some identities on the weighted Euler numbers and polynomials. In other words, the authors investigate systematically the class of Sheffer sequences in connection with the generating function of the weighted Euler polynomials.
MSC:
| 11B68 | Bernoulli and Euler numbers and polynomials |
| 11S80 | Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.) |
Keywords:
Appell sequence; Sheffer sequence; Euler number; Euler polynomial; formal power series; fermionic \(p\)-adic integral on \( \mathbb{Z}_{p} \); umbral calculusReferences:
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