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

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.

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Correspondence to Mumtaz Riyasat.

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This work has been done under Post-Doctoral Fellowship (Office Memo No.2/40(38)/2016/R&D-II/1063) awarded to Dr. Mumtaz Riyasat by the National Board of Higher Mathematics, Department of Atomic Energy, Government of India, Mumbai, and Senior Research Fellowship (Award letter no. F./2014-15/NFO-2014-15-OBC-UTT-24168/(SA-III/Website)) awarded to Ms. Tabinda Nahid by the University Grants Commission, Government of India, New Delhi.

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Khan, S., Nahid, T. & Riyasat, M. Partial derivative formulas and identities involving \(\mathbf {2}\)-variable Simsek polynomials. Bol. Soc. Mat. Mex. 26, 1–13 (2020). https://doi.org/10.1007/s40590-019-00236-4

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Keywords

  • Partial differential equations
  • Recurrence relations
  • 2-variable Simsek polynomials

Mathematics Subject Classification

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