Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

A NEW CLASS OF q-HERMITE-BASED APOSTOL TYPE FROBENIUS GENOCCHI POLYNOMIALS

  • Kang, Jung Yoog (Department of Mathematics Education Silla University) ;
  • Khan, Waseem A. (Department of Mathematics and Natural Sciences Prince Mohammad Bin Fahd University)
  • Received : 2019.12.18
  • Accepted : 2020.05.22
  • Published : 2020.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this article, a hybrid class of the q-Hermite based Apostol type Frobenius-Genocchi polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating function methods. Furthermore, we consider some relationships for q-Hermite based Apostol type Frobenius-Genocchi polynomials of order α associated with q-Apostol Bernoulli polynomials, q-Apostol Euler polynomials and q-Apostol Genocchi polynomials.

Keywords

References

  1. W. A. Al-Salam, q-Appell polynomials, Ann. Mat. Pura Appl. (4) 77 (1967), 31-45. https://doi.org/10.1007/BF02416939
  2. G. E. Andrews, R. Askey, and R. Roy, Special Functions, Encyclopedia of Mathematics and its Applications, 71, Cambridge University Press, Cambridge, 1999. https://doi.org/10.1017/CBO9781107325937
  3. G.-S. Cheon and J.-H. Jung, The q-Sheffer sequences of a new type and associated orthogonal polynomials, Linear Algebra Appl. 491 (2016), 171-186. https://doi.org/10.1016/j.laa.2015.07.008
  4. U. Duran, M. Acikgoz, and S. Araci, On higher order (p, q)-Frobenius-Euler polynomials, TWMS J. Pure Appl. Math. 8 (2017), no. 2, 198-208.
  5. M. Eini Keleshteri and N. I. Mahmudov, A study on q-Appell polynomials from determinantal point of view, Appl. Math. Comput. 260 (2015), 351-369. https://doi.org/10.1016/j.amc.2015.03.017
  6. M. Eini Keleshteri and N. I. Mahmudov, On the class of 2D q-Appell polynomials, arXiv:1512.03255v1.
  7. B. Kurt, A note on the Apostol type q-Frobenius-Euler polynomials and generalizations of the Srivastava-Pinter addition theorems, Filomat 30 (2016), no. 1, 65-72. https://doi.org/10.2298/FIL1601065K
  8. N. I. Mahmudov, On a class of q-Bernoulli and q-Euler polynomials, Adv. Difference Equ. 2013 (2013), 108, 11 pp. https://doi.org/10.1186/1687-1847-2013-108
  9. N. I. Mahmudov, Difference equations of q-Appell polynomials, Appl. Math. Comput. 245 (2014), 539-543. https://doi.org/10.1016/j.amc.2014.07.107
  10. N. I. Mahmudov and M. E. Keleshteri, q-extensions for the Apostol type polynomials, J. Appl. Math. 2014 (2014), Art. ID 868167, 8 pp. https://doi.org/10.1155/2014/868167
  11. N. I. Mahmudov and M. Momenzadeh, On a class of q-Bernoulli, q-Euler, and q-Genocchi polynomials, Abstr. Appl. Anal. 2014 (2014), Art. ID 696454, 10 pp. https://doi.org/10.1155/2014/696454
  12. 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), no. 3, 679-695. https://doi.org/10.1007/s00009-014-0423-0
  13. M. A. Pathan and W. A. Khan, A new class of generalized polynomials associated with Hermite and Euler polynomials, Mediterr. J. Math. 13 (2016), no. 3, 913-928. https://doi.org/10.1007/s00009-015-0551-1
  14. M. Riyasat and S. Khan, Some results on q-Hermite based hybrid polynomials, Glas. Mat. Ser. III 53(73) (2018), no. 1, 9-31. https://doi.org/10.3336/gm.53.1.02
  15. H. M. Srivastava and H. L. Manocha, A treatise on generating functions, Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester, 1984.
  16. B. Yilmaz Yasar and M. A. Ozarslan, Frobenius-Euler and Frobenius-Genocchi polynomials and their differential equations, New Trends Math. Sci. 3 (2015), no. 2, 172-180.