A Note on the Truncated-Exponential Based Apostol-Type Polynomials

• Main Authors: H. M. Srivastava, Serkan Araci, Waseem A. Khan, Mehmet Acikgöz
• Format: Article
• Language: English
• Published: MDPI AG 2019-04-01
• Series: Symmetry
• Subjects: truncated-exponential polynomials; monomiality principle; generating functions; Apostol-type polynomials and Apostol-type numbers; Bernoulli, Euler and Genocchi polynomials; Bernoulli, Euler, and Genocchi numbers; operational methods; summation formulas; symmetric identities
• Online Access: https://www.mdpi.com/2073-8994/11/4/538

In this paper, we propose to investigate the truncated-exponential-based Apostol-type polynomials and derive their various properties. In particular, we establish the operational correspondence between this new family of polynomials and the familiar Apostol-type polynomials. We also obtain some implicit summation formulas and symmetric identities by using their generating functions. The results, which we have derived here, provide generalizations of the corresponding known formulas including identities involving generalized Hermite-Bernoulli polynomials.