Integrals of Lagrange functions and sum rules
نویسنده
چکیده
Exact values are derived for some matrix elements of Lagrange functions, i.e. orthonormal cardinal functions, constructed from orthogonal polynomials. They are obtained with exact Gauss quadratures supplemented by corrections. In the particular case of Lagrange-Laguerre and shifted Lagrange-Jacobi functions, sum rules provide exact values for matrix elements of 1/x and 1/x as well as for the kinetic energy. From these expressions, new sum rules involving Laguerre and shifted Jacobi zeros and weights are derived. PACS numbers: 03.65.-w, 02.70.Hm, 02.70.Jn, 02.30.Gp Submitted to: J. Phys. A: Math. Gen. 20 April 2011
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