Numerical Quadrature Rules for Some Infinite Range Integrals
نویسندگان
چکیده
Recently the present author has given a new approach to numerical quadrature and derived new numerical quadrature formulas for finite range integrals with algebraic and/or logarithmic endpoint singularities. In the present work this approach is used to derive new numerical quadrature formulas for integrals of the form J"£" x"e~xf(x) dx and J"o° x"Ep(x)f(x) dx, where Ef(x) is the exponential integral. It turns out the new rules are of interpolator/ type, their abscissas are distinct and he in the interval of integration and thenweights, at least numerically, are positive. For fixed a the new integration rules have the same set of abscissas for all p. Finally, the new rules seem to be at least as efficient as the corresponding Gaussian quadrature formulas. As an extension of the above, numerical quadrature formulas for integrals of the form ff" \x\^e'xf(x) dx too are considered.
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