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A Note on Finite Quadrature Rules with a Kind of Freud Weight Function

2009; Hindawi Publishing Corporation; Volume: 2009; Issue: 1 Linguagem: Inglês

10.1155/2009/421546

1563-5147

Kamal Aghigh, Mohammad Masjed‐Jamei,

Iterative Methods for Nonlinear Equations

We introduce a finite class of weighted quadrature rules with the weight function |x| −2 a exp (−1/ x 2 ) on (− ∞ , ∞ ) as , where x i are the zeros of polynomials orthogonal with respect to the introduced weight function, w i are the corresponding coefficients, and R n [ f ] is the error value. We show that the above formula is valid only for the finite values of n . In other words, the condition a ≥ {max n } + 1/2 must always be satisfied in order that one can apply the above quadrature rule. In this sense, some numerical and analytic examples are also given and compared.