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The main purpose of this paper is to investigate the $q$-Apostol type Frobenius-Euler numbers and polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive $q$-integers. By using infinite series representation for $q$-Apostol type Frobenius-Euler numbers and polynomials including their interpolation functions, we not only give some identities and relations for these numbers and polynomials, but also define generating functions for new numbers and polynomials. Further we give remarks and observations on generating functions for these new numbers and polynomials. By using these generating functions, we derive recurrence relations and finite sums related to these numbers and polynomials. Moreover, by applying higher-order derivative to these generating functions, we derive some new formulas including the Hurwitz--Lerch zeta function, the Apostol-Bernoulli numbers and the Apostol-Euler numbers. Finally, for an application of the generating functions, we derive a multiplication formula, which is very important property in the theories of normalized polynomials and Dedekind type sums.
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참고문헌 (34)
참고문헌 신청
M. Alkan / 2013 / Generating function for q-Eulerian polynomials and their decomposition and applications / Fixed Point Theory Appl 2013:14
T. M. Apostol / 1951 / On the Lerch zeta function / Pacific J. Math 1:161~167
A. Bayad / 2016 / Identities for Apostol-type Frobenius-Euler polynomials resulting from the study of a nonlinear operator / Russ. J. Math. Phys 23(2):164~171
I. N. Cangul / 2015 / GENERALIZATION OF q-APOSTOL-TYPE EULERIAN NUMBERS AND POLYNOMIALS, AND THEIR INTERPOLATION FUNCTIONS / Advanced Studies in Contemporary Mathematics 25(2):211~220
R. Dere / 2013 / Normalized polynomials and their multiplication formulas / Adv. Difference Equ 2013(31):10
T. M. Apostol / 1951 / On the Lerch zeta function / Pacific J. Math 1:161~167
A. Bayad / 2016 / Identities for Apostol-type Frobenius-Euler polynomials resulting from the study of a nonlinear operator / Russ. J. Math. Phys 23(2):164~171
I. N. Cangul / 2015 / GENERALIZATION OF q-APOSTOL-TYPE EULERIAN NUMBERS AND POLYNOMIALS, AND THEIR INTERPOLATION FUNCTIONS / Advanced Studies in Contemporary Mathematics 25(2):211~220
R. Dere / 2013 / Normalized polynomials and their multiplication formulas / Adv. Difference Equ 2013(31):10
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