On the Analogs of Bernoulli and Euler Numbers, Related Identities and Zeta and L-Functions

Identities Associated with Generalized Stirling Type Numbers and Eulerian Type Polynomials

“…It is known that The p -adic q -integral is used in many branch of mathematics, mathematical physics and other areas (cf. [8], [10], [22], [23], [26], [27], [34]). …”

A study on a class of q-Euler polynomials under the symmetric group of degree n

“…Motivated by the paper of Kim et al [10], we study q-extension of λ-Euler polynomials earlier given by Kim et al [9]. We derive some new symmetric identities for these polynomials, using fermionic p-adic invariant integral over the p-adic number field introduced by Kim [6], under symmetric group of degree n denoted by S n .…”

“…(1.3) yields E n,q (λ, 0) := E n,q (λ) called n-th q-extension of λ−Euler numbers, cf. [9]. By taking q → 1 − in the Eq.…”

“…In [9], Kim et al defined q-extension of λ-Euler polynomials by the following fermionic p-adic integral on Z p :…”

A New Class of Laguerre-based Generalized Apostol Polynomials

“…where E n (x) denotes the classical Euler polynomials (see from example [5], [6], [7], [9], [12], [31]- [33], [35]- [40]; see also the reference cited in each of these earlier works).…”