Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4637360 | Applied Mathematics and Computation | 2006 | 7 Pages |
Abstract
A class of weighted quadrature rules whose weight function corresponds to T distribution, i.e. K(1+x2)-(p-12),xâ(-â,â), is introduced and investigated. The integration formulas, given in this work, are generally in the following form:â«-ââ(1+x2)-(p-12)f(x)dx=âi=1nwif(xi)+Rn[f],where xi is the zeros of orthogonal polynomials with respect to the introduced weight function, wi is the related coefficient and Rn[f] is the error function. It is important to point out that the above mentioned formula is valid only for the finite values of n. In other words, p > {max n} + 1 must be satisfied in order that the above integration formula is applicable. Some analytical examples are finally given and compared.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
E. Babolian, M. Masjed-Jamei, M.R. Eslahchi, Mehdi Dehghan,