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On Generating Functions for Boole Type Polynomials and Numbers of Higher Order and Their Applications

by Yilmaz Simsek 1 and Ji Suk So 2,*
1
Department of Mathematics, Faculty of Science, Akdeniz University, TR-07058 Antalya, Turkey
2
Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University, Chonju, Chonbuk 561-756, Korea
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(3), 352; https://doi.org/10.3390/sym11030352
Received: 1 February 2019 / Revised: 1 March 2019 / Accepted: 2 March 2019 / Published: 8 March 2019
The purpose of this manuscript is to study and investigate generating functions for Boole type polynomials and numbers of higher order. With the help of these generating functions, many properties of Boole type polynomials and numbers are presented. By applications of partial derivative and functional equations for these functions, derivative formulas, recurrence relations and finite combinatorial sums involving the Apostol-Euler polynomials, the Stirling numbers and the Daehee numbers are given. View Full-Text
Keywords: Apostol-Euler polynomials and numbers; Peters polynomials and numbers; Boole polynomials and numbers; Stirling numbers; Daehee numbers; generating functions; Changheenumbers and polynomials Apostol-Euler polynomials and numbers; Peters polynomials and numbers; Boole polynomials and numbers; Stirling numbers; Daehee numbers; generating functions; Changheenumbers and polynomials
MDPI and ACS Style

Simsek, Y.; So, J.S. On Generating Functions for Boole Type Polynomials and Numbers of Higher Order and Their Applications. Symmetry 2019, 11, 352.

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