a note on finite quadrature rules with a kind of freud weight function
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ID: 154975
2009
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Abstract
We introduce a finite class of weighted quadrature rules with the
weight function |x|โ2๐exp(โ1/๐ฅ2) on (โโ,โ) as
โซโโโ|๐ฅ|โ2๐exp(โ1/๐ฅ2โ)๐(๐ฅ)๐๐ฅ=๐๐=1๐ค๐๐(๐ฅ๐)+๐
๐[๐], where ๐ฅ๐ are the zeros of polynomials orthogonal with respect to the introduced weight
function, ๐ค๐ are the corresponding coefficients, and ๐
๐[๐] is the error value. We show that the
above formula is valid only for the finite values of ๐. In other words, the condition ๐โฅ{max๐}+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.
| Reference Key |
aghigh2009mathematicala
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|---|---|
| Authors | ;Kamal Aghigh;M. Masjed-Jamei |
| Journal | journal of power sources |
| Year | 2009 |
| DOI |
10.1155/2009/421546
|
| URL | |
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