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Differentiation by integration with Jacobi polynomials
Numerical differentiation Ill-pose problems Jacobi orthogonal polynomials Orthogonal series
2011/2/28
In this paper, the numerical differentiation by integration method based on Jacobi polynomials originally introduced by Mboup, Fliess and Join [20, 21] is revisited in the central case where the used ...
We study a new family of "classical" orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with differential operators of Dunkl-type. These polynomials ...
Properties of the exceptional ($X_{\ell}$) Laguerre and Jacobi polynomials
Jacobi polynomials ($X_{\ell}$) Laguerre
2010/4/7
We present various results on the properties of the four infinite sets of the exceptional $X_{\ell}$ polynomials discovered recently (Odake and Sasaki, Phys. Lett. {\bf B679} (2009) 414-417). These $X...
Infinitely many shape invariant potentials and cubic identities of the Laguerre and Jacobi polynomials
invariant potentials Jacobi polynomials cubic identities
2010/4/8
We provide analytic proofs for the shape invariance of the recently discovered (Odake and Sasaki, Phys. Lett. B679 (2009) 414-417) two families of infinitely many exactly solvable one-dimensional quan...
Local Estimates for Jacobi Polynomials.