Notes on Unified q-Apostol-Type Polynomials

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KURT B.

FILOMAT, vol.30, no.4, pp.921-927, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.2298/fil1604921k
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.921-927
  • Keywords: Bernoulli numbers and polynomials, Euler polynomials and numbers, generating function, generating function, Apostol-Bernoulli number and polynomials, generalized q-Bernoulli polynomials, generalized q-Genocchi polynomials, Q-EXTENSIONS, BERNOULLI, EULER
  • Akdeniz University Affiliated: Yes

Abstract

Recently, many mathematicians (Karande and Thakare [6], Ozarslan [14], Ozden et. al. [15], El-Deouky et. al. [5]) have studied the unification of Bernoulli, Euler and Genocchi polynomials. They gave some recurrence relations and proved some theorems. Mahmudov [13] defined the new q-Apostol-Bernoulli and q-Apostol-Euler polynomials. Also he gave the analogous of the Srivastava-Pinter addition theorems. Kurt [8] gave the new identities and some relations for these polynomials. In this work, we give some recurrence relations for the unified q-Apostol-type polynomials related to multiple sums. By using generating functions we derive many new identities and recurrence relations associated with the q-Apostol-type Bernoulli, the q-Apostol-type Euler and the q-Apostol-type Genocchi polynomials and numbers and also the generalized Stirling type numbers of the second kind.