Certain Properties of Apostol-Type Hermite-Based- Frobenius-Genocchi Polynomials
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Authors: W. A. KHAN AND D. SRIVASTAVA
DOI: 10.46793/KgJMat2106.859K
Abstract:
This paper is well designed to set-up some new identities related to generalized Apostol-type Hermite-based-Frobenius-Genocchi polynomials and by applying the generating functions, we derive some implicit summation formulae and symmetric identities. Further a relationship between Array-type polynomials, Apostol-type Bernoulli polynomials and generalized Apostol-type Frobenius-Genocchi polynomials is also established.
Keywords:
Hermite polynomials, Frobenius-Genocchi polynomials, Apostol-type Hermite-based Genocchi polynomials.
References:
[1] E. T. Bell, Exponential polynomials, Ann. of Math. 35 (1934), 258–277.
[2] G. Dattoli, S. Lorenzutt and C. Cesarano, Finite sums and generalized forms of Bernoulli polynomials, Rendiconti di Mathematica 19 (1999), 385–391.
[3] B. Kurt and Y. Simsek, On the generalized Apostol-type Frobenius-Euler polynomials, Adv. Difference Equ. 2013(1) (2013), 1–9.
[4] D. S. Kim and T. Kim, Some identities of degenerate special polynomials, Open Math. 13 (2015), 380–389.
[5] W. A. Khan, S. Araci, M. Acikgoz and H. Haroon, A new class of partially degenerate Hermite-Genocchi polynomials, J. Nonlinear Sci. Appl. 10 (2017), 5072–5081.
[6] W. A. Khan, Some properties of the generalized Apostol-type Hermite-based polynomials, Kyungpook Math. J. 55 (2015), 597–614.
[7] W. A. Khan and H. Haroon, Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials, Springerplus 5(1) (2016), 1–21.
[8] Q. M. Luo, B. N. Guo, F. Qi and L. Debnath, Generalization of Bernoulli numbers and polynomials, Int. J. Math. Math. Sci. 59 (2003), 3769–3776.
[9] Q. M. Luo, B. N. Guo, F. Qi and L. Debnath, Generalization of Euler numbers and polynomials, Int. J. Math. Math. Sci. 61 (2003), 3893–3901.
[10] M. A. Pathan and W. A. Khan, Some implicit summation formulas and symmetric identities for the generalized Hermite-Bernoulli polynomials, Mediterr. J. Math. 12 (2015), 679–695.
[11] M. A. Pathan and W. A. Khan, A new class of generalized polynomials associated with Hermite and Euler polynomials, Mediterr. J. Math. 13(3) (2016), 913–928.
[12] M. A. Pathan and W. A. Khan, Some new classes of generalized Hermite-based Apostol-Euler and Apostol-Genocchi polynomials, Fasc. Math. 55(1) (2015), 153–170.
[13] Y. Simsek, Generating functions for generalized Striling type numbers, Array type polynomials, Eulerian type polynomials and their applications, Fixed Point Theory Appl. (2013), DOI 1186/1687-1812-2013-87.
[14] Y. Simsek, Generating Functions for q-Apostol type Frobenius-Euler numbers and polynomials, Axioms 1 (2012), 395–403.
[15] H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Ellis Horwood Limited. Co. New York, 1984.
[16] H. M. Srivastava, M. Garg and S. A. Choudhari, New generalization of the Bernoulli and related polynomials, Russ. J. Math. Phy. 17 (2010), 251–261.
[17] B. Y. Yaşar and M. A. Özarslan, Frobenius-Euler and Frobenius-Genocchi polynomials and their differential equations, New Trends Math. Sci. 3(2) (2015), 172–180.
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