- Volume 55 Issue 3
In this paper, we study some properties of the generalized Apostol type Hermite-based polynomials. which extend some known results. We also deduce some properties of the generalized Apostol-Bernoulli polynomials, the generalized Apostol-Euler polynomials and the generalized Apostol-Genocchi polynomials of high order. Numerous properties of these polynomials and some relationships between
Hermite polynomials;generalized Apostol type Hermite-based polynomials;summation formulae
- A. Erdelyi, W. Magnus, F. Oberhettinger and F. Tricomi, Higher transcendental functions, vols. 1-3, (1953).
- D. Q. Lu and Q. M. Luo, Some properties of the generalized Apostol tpe polynomials, Boundary Value Problems., (2013),2013:64. https://doi.org/10.1186/1687-2770-2013-64
- E. T. Bell, Exponential polynomials, Ann. of Math., 35(1943), 258-277.
- E. R. Hansen, A table of series and products, Printice Hall, Englewood Cliffs, NJ, (1975).
- F. Magnus, W. Oberhettinger and R. P. Soni, Some formulas and theorem for the special functions of mathematical physics, Third enlarged edition, Springer-Verlag, New York, (1966).
- G. Dattoli, S. Lorenzutt and C. Cesarano, Finite sums and generalized forms of Bernoulli polynomials,Rendiconti di Mathematica, 19(1999), 385-391.
- H. M. Srivastava and H. L .Manocha, A treatise on generating functions, Ellis Horwood Limited. Co. New York, (1984).
- H. M. Srivastava, M. Garg and S. Choudhary, A new generalization of the Bernoulli and related polynomials, Russian J. Math. Phys, 17(2010), 251-261. https://doi.org/10.1134/S1061920810020093
- H. M. Srivastava, M. Garg and S. Choudhary, Some new families of generalized Euler and genochhi polynomials, Taiwanese J. Math, 15(1)(2011), 283-305.
- H. Yang, An identity of symmetry for the Bernoulli polynomials, Discrete Math. (2007)dol:10:10,16/j.disc 2007.03.030.
- L. Comlet, The art of finite and infinite expansions, (Translated from french by J. W. Nilenhuys), Reidel, Dordrecht, 1974.
- M. Abramowitz and I. A. Stegun, Handbook of mathematical functions with formulas graphs and mathematical tables, National Bureau of Standards, Washington, DC, 1964.
- M. A. Pathan, A new class of generalized Hermite-Bernoulli polynomials, Georgian Mathematical Journal, 19(2012), 559-573.
- M. A. Pathan and W. A. Khan, Some implicit summation formulas and symmetric identities for the generalized Hermite-Bernoulli polynomials, Mediterr.J.Math.(2014),DOI 10.1007/s00009-014-0423-0, Springer Basel 2014. https://doi.org/10.1007/s00009-014-0423-0
- Q. M. Luo, Apostol Euler polynomials of higher order and gaussian hypergeometric functions, Taiwanese J. Math., 10(4)(2006), 917-925.
- Q. M. Luo, q-extensions for the Apostol-Genocchi polynomials, Gen. Math., 17(2)(2009), 113-125.
- Q. M. Luo, Extensions 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(1)(2005), 290-302. https://doi.org/10.1016/j.jmaa.2005.01.020
- Q. M. Luo and H. M. Srivastava, Some generalizations of the Apostol Genocchi polynomials and the stirling number of the second kind, Appl. Math. Comput, 217(2011), 5702-5728. https://doi.org/10.1016/j.amc.2010.12.048
- Q. M. Luo and H. M. Srivastava, Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials, Comput. Math. Appl, 51(2006), 631-642. https://doi.org/10.1016/j.camwa.2005.04.018
- S. Khan, M. A. Pathan, N. A. M. Hassan, G. Yasmin , Implicit summation formula for Hermite and related polynomials, J. Math. Anal. Appl, 344(2008), 408-416. https://doi.org/10.1016/j.jmaa.2008.02.052
- S. L. Yang and Z. K. Qiao, Some symmetry identities for the Euler polynomials, J. Math. Resrch. Exposition, 30(3)(2010), 457-464.
- Y. Luke, The special functions and their approximations, vols, 1-2, 1969.
- Yu. A. Brychkov, On multiple sums of special functions, Integral Trans. Spec. Func., 21(12)(2010), 877-884. https://doi.org/10.1080/10652469.2010.480846
- Z. Zhang and H. Yang, Several identities for the generalized Apostol Bernoulli polynomials, Computers and Mathematics with Applications, 56(2008), 2993-2999. https://doi.org/10.1016/j.camwa.2008.07.038
- A new generalization of Apostol type Hermite–Genocchi polynomials and its applications vol.5, pp.1, 2016, https://doi.org/10.1186/s40064-016-2357-4