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Generalized fractional operator representations of Jacobi type orthogonal polynomials

133   0   0.0 ( 0 )
 Added by K S Nisar Dr
 Publication date 2017
  fields
and research's language is English
 Authors K. S. Nisar




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The aim of this paper is to apply generalized operators of fractional integration and differentiation involving Appells function $F_{3}(:)$ due to Marichev-Saigo-Maeda (MSM), to the Jacobi type orthogonal polynomials. The results are expressed in terms of generalized hypergeometric function. Some of the interesting special cases of the main results also established.



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The present paper is about Bernstein-type estimates for Jacobi polynomials and their applications to various branches in mathematics. This is an old topic but we want to add a new wrinkle by establishing some intriguing connections with dispersive estimates for a certain class of Schrodinger equations whose Hamiltonian is given by the generalized Laguerre operator. More precisely, we show that dispersive estimates for the Schrodinger equation associated with the generalized Laguerre operator are connected with Bernstein-type inequalities for Jacobi polynomials. We use known uniform estimates for Jacobi polynomials to establish some new dispersive estimates. In turn, the optimal dispersive decay estimates lead to new Bernstein-type inequalities.
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