Implicit Summation Formula for 2-Variable Laguerre-Based Poly-Genocchi Polynomials

Main Article Content

Waseem A. Khan, Idrees A. Khan, Moin Ahmad

Abstract

The main object of this paper is to introduce a new class of Laguerre-based poly-Genocchi polynomials and investigate some properties for these polynomials and related to the Stirling numbers of the second kind. We derive summation formulae and general symmetry identities by using different analytical means and applying generating functions.

Article Details

References

  1. L. C. Andrews, Special functions for engineers and mathematicians, Macmillan Co. New York, 1985.
  2. A. Bayad and Y. Hamahata, Polylogarithms and poly-Bernoulli polynomials, Kyushu. J. Math. 65(2011), 15-24.
  3. C. H. Chang and C. W. Ha, On recurrence relation for Bernoulli and Euler numbers, Bull. Aust. Math. Soc. 64(2001), 469-474.
  4. G. S. Cheon, A note on the Bernoulli and Euler polynomials, App. Math. Lett. 16(3)(2003), 365-368.
  5. G. Dattoli, A. Torre, Operational methods and two variable Laguerre polynomials, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 132(1998) 3-9.
  6. G. Dattoli, A. Torre and A. M. Mancho, The generalized Laguerre polynomials, the associated Bessel functions and applications to propagation problems, Radiat. Phys. Chem. 59(2000), 229-237.
  7. H. Jolany, M. R. Darafsheh, R. E. Alikelaye, Generalizations of Poly-Bernoulli Numbers and Polynomials, Int. J. Math. Comb. 2(2010), 7-14.
  8. H. Jolany, R. B. Corcino, Explicit formula for generalization of Poly-Bernoulli numbers and polynomials with a,b,c parameters, J. Class. Anal. 6(2015), 119-135.
  9. H. Jolany, M. Aliabadi, R. B. Corcino and M. R. Darafsheh, A Note on Multi Poly-Euler Numbers and Bernoulli Polynomials, Gen. Math. 20(2-3)(2012), 122-134.
  10. M. Kaneko, Poly-Bernoulli numbers, J. Thor. Nombres Bordx. 9 (1997), 221-228.
  11. W. A. Khan, Some properties of the generalized Apostol type Hermite-Based polynomials, Kyungpook Math. J. 55(2015), 597-614.
  12. W. A. Khan, A note on Hermite-based poly-Euler and multi poly-Euler polynomials, Palestine J. Math. 6(2017), 204-214.
  13. W. A. Khan, S. Araci, M. Acikgoz, A new class of Laguerre-based Apostol type polynomials, Cogent Math. 3(2016), Art. ID 1243839.
  14. T. Kim, Y. S. Jang and J. J. Seo, A note on poly-Genocchi numbers and polynomials, Appl. Math. Sci. 8(2014), 4475-4781.
  15. M. A. Pathan and W. A. Khan, Some implicit summation formulas and symmetric identities for the generalized HermiteEuler polynomials, East-West J. Math. 16(1) (2014), 92-109.
  16. H. M. Srivastava and H. L. Manocha, A treatise on generating functions Ellis Horwood Limited, New York, 1984.