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In this paper, a new form of poly-Genocchi polynomials is defined by means of polylogarithm, namely, the Apostol-type poly-Genocchi polynomials of higher order with parameters $a$, $b$ and $c$. Several properties of these polynomials are established including some recurrence relations and explicit formulas, which are used to express these higher order Apostol-type poly-Genocchi polynomials in terms of Stirling numbers of the second kind, Apostol-type Bernoulli and Frobenius polynomials of higher order. Moreover, certain differential identity is obtained that leads this new form of poly-Genocchi polynomials to be classified as Appell polynomials and, consequently, draw more properties using some theorems on Appell polynomials. Furthermore, a symmetrized generalization of this new form of poly-Genocchi polynomials that possesses a double generating function is introduced. Finally, the type 2 Apostol-poly-Genocchi polynomials with parameters $a$, $b$ and $c$ are defined using the concept of polyexponential function and several identities are derived, two of which show the connections of these polynomials with Stirling numbers of the first kind and the type 2 Apostol-type poly-Bernoulli polynomials.
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참고문헌 (19)
참고문헌 신청
Serkan Araci / 2014 / THEOREMS ON GENOCCHI POLYNOMIALS OF HIGHER ORDER ARISING FROM GENOCCHI BASIS / Taiwanese Journal of Mathematics 18(2):473~482
Abdelmejid Bayad / 2011 / Arakawa–Kaneko L-functions and generalized poly-Bernoulli polynomials / Journal of Number Theory 131(6):1020~1036
J. Choi / 2019 / Certain unified polynomials / Integral Transforms Spec. Funct 3(1):28~40
Y. He / 2017 / Some new results on products of the Apostol-Genocchi polynomials / J. Comput. Anal. Appl 2(4,):591~600
Hassan Jolany / 2012 / Explicit formula for generalization of poly-Bernoulli numbers and polynomials with a,b,c parameters / Journal of Classical Analysis 6(2):119~135
Abdelmejid Bayad / 2011 / Arakawa–Kaneko L-functions and generalized poly-Bernoulli polynomials / Journal of Number Theory 131(6):1020~1036
J. Choi / 2019 / Certain unified polynomials / Integral Transforms Spec. Funct 3(1):28~40
Y. He / 2017 / Some new results on products of the Apostol-Genocchi polynomials / J. Comput. Anal. Appl 2(4,):591~600
Hassan Jolany / 2012 / Explicit formula for generalization of poly-Bernoulli numbers and polynomials with a,b,c parameters / Journal of Classical Analysis 6(2):119~135
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