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Generalized Hermite-Based Apostol-Bernoulli, Euler, Genocchi Polynomials and their Relations
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In this paper, we have generalized Apostol-Hermite-Bernoullli polynomials, Apostol-Hermite-Euler polynomials and Apostol-Hermite-Genocchi polynomials. We have shown that there is an intimate connection between these polynomials and derived some implicit summation formulae by applying the generating functions
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2010 Mathematics Subject Classification. Primary 54C40, 14E20; Secondary 46E25, 20C20.
Apostol-Hermite-Bernoullli Polynomials, Apostol-Hermite-Euler Polynomials and Apostol-Hermite-Genocchi Polynomials, Summation Formulae, Symmetric Identities.
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- T. M. Apostol, On the Lerch Zeta function, Pacific J. Math., 1(1951), 161-167.
- E. T. Bell, Exponential polynomials, Ann. Math., 35(1934), 258-277.
- G. Dattoli, B. Germano and P. E. Ricci, Hermite polynomials with more than two variables and associated bi-orthogonal functions, Integral Transforms and Special Functions, 20(1) (2009), 17-22.
- Q. M. Luo, Fourier expansions and integral representations for the Apostol-Bernoulli and ApostolEuler polynomials, Math. of Comp. 78 (2009), 2193-2208.
- Q. M. Luo, Fourier expansions and integral representations for the Genocchi polynomials, J. Integer Seq. 12 (2009), 1-9.
- Q. M. Luo, q-extension for the Apostol-Genocchi polynomials, Gen. Math. 17 (2009), 113-125.
- Q. M. Luo, Some formulas for the Apostol-Euler polynomials associated with Hurwitz zeta function at rational arguments, Applicable Analysis and Discrete Mathematics 3(2) (2009), 336-346.
- Q. M. Luo, The multiplication formulas for the Apostol-Bernoulli and Apostol-Euler polynomials of higher order, Integral Transform and Special Functions, 20(5-6) (2009), 377-391.
- Q. M. Luo, Extension for the Genocchi polynomials and its Fourier expansions and integral representations, Osaka J. Math. 48 (2011), 291-310.
- Q. M. Luo and H. M. Srivastava, Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials, J. Math. Anal. Appl., 308(2005), 290-302.
- Q. M. Luo and H. M. Srivastava, Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials, Computers and Mathematics with Applications, 51(3-4) (2006), 631-642.
- Q. M. Luo and H. M. Srivastava, Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind, Applied Math. & Comput. 217(12) (2011), 5702-5728.
- M. A. O¨ zarslan, Hermite-based unified Apostol-Bernoulli, Euler and Genocchi polynomials, Adv. Diff. Eq. (2013), 116, DOI: 10.1186/1687-1847-2013-116.
- M. A. Pathan and W. A. Khan, Some new classes of generalized Hermite-based Apostol-Euler and Apostol-Genocchi polynomials, Fasciculi Mathematici, 55(2015), 153-170, DOI: 10.1515/fascmath2015-0020.
- E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960.
- H. M. Srivastava and H. L. Manocha, Atreatise on Generating Functions, Halsted, New York, 1984.
- H. M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc. 129 (2000), 77-84.
- R. Tremblay, S. Gaboury and B. J. Fugere, Some new classes of generalized Apostol-Euler and Apostol-Genocchi polynomials, Int. J. Math and Math. Sci. (2012), DOI:10.1155/2012/182785.
- R. Tremblay, S. Gaboury and B. J. Fugere, A further generalization of Apostol-Bernoulli polynomials and related polynomials, Honam Math. J. 34 (2012), 311-326.
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