Differential and integral equations for Legendre – Laguerre based hybrid polynomials

  • S. Khan Aligarh Muslim Univ., India
  • M. Riyasat Zakir Hussain College Eng. and Technology, Aligarh Muslim Univ., India
  • Sh. A. Wani Univ. Kashmir, Srinagar, India
Keywords: Legendre-Laguerre polynomials, Appell polynomials, Legendre-Laguerre-Appell polynomials, Recurrence relations, Differential equations, Integral equations

Abstract

UDC 517.9

 In this article, a hybrid family of three-variable Legendre – Laguerre – Appell polynomials is explored and their properties including the series expansions, determinant forms, recurrence relations, shift operators, followed by differential, integro-differential and partial differential equations are established.
The analogous results for the three-variable Hermite – Laguerre – Appell polynomials are deduced. Certain examples in terms of Legendre – Laguerre – Bernoulli, –E uler and – Genocchi polynomials are constructed to show the applications of main results. A further investigation is performed by deriving homogeneous Volterra integral equations for these polynomials and for their relatives.


Author Biography

S. Khan, Aligarh Muslim Univ., India




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Published
19.03.2021
How to Cite
Khan, S., M. Riyasat, and S. A. Wani. “Differential and Integral Equations for Legendre – Laguerre Based Hybrid Polynomials”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 3, Mar. 2021, pp. 408 -24, doi:10.37863/umzh.v73i3.894.
Section
Research articles