Advertisement

Partial derivative formulas and identities involving \(\mathbf {2}\)-variable Simsek polynomials

  • Subuhi Khan
  • Tabinda Nahid
  • Mumtaz RiyasatEmail author
Original Article
  • 16 Downloads

Abstract

The 2-variable Simsek polynomials \(Y_n(x,y;\lambda , \delta )\) are introduced as the generalization of a new family of polynomials \(Y_n(x;\lambda )\). Certain partial derivatives formulas and identities for the 2-variable Simsek polynomials \(Y_n(x,y;\lambda , \delta )\) are established. A brief view of quasi-monomial approach establishing differential operators and equation is presented for these polynomials.

Keywords

Partial differential equations Recurrence relations 2-variable Simsek polynomials 

Mathematics Subject Classification

Primary 05A10 05A15 11B37 11B68 11B83 Secondary 33C05 

Notes

References

  1. 1.
    Dattoli, G.: Hermite-Bessel and Laguerre-Bessel functions: a by-product of the monomiality principle, Advanced Special Functions and Applications (Melfi, 1999), 147–164, Proc. Melfi Sch. Adv. Top. Math. Phys., vol. 1, Aracne (2000)Google Scholar
  2. 2.
    Subuhi Khan, T. Nahid, M. Riyasat, Properties and graphical representations of the 2-variable form of the Simsek polynomials. J. Number Theory (submitted) Google Scholar
  3. 3.
    Kim, T.: Daehee numbers and polynomials. Appl. Math. Sci. (Ruse) 7, 5969–5976 (2013)MathSciNetGoogle Scholar
  4. 4.
    Simsek, Y.: Construction of some new families of Apostol-type numbers and polynomials via Dirichlet character and \(p\)-adic \(q\)-integral. Turk. J. Math. 42, 557–577 (2018)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Steffensen, J.F.: The poweroid, an extension of the mathematical notion of power. Acta Math. 73, 333–366 (1941)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Sociedad Matemática Mexicana 2019

Authors and Affiliations

  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia

Personalised recommendations