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Mathematics of Computation

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Movable singularities and quadrature


Authors: R. F. Goodrich and F. Stenger
Journal: Math. Comp. 24 (1970), 283-300
MSC: Primary 65.55
DOI: https://doi.org/10.1090/S0025-5718-1970-0275669-4
MathSciNet review: 0275669
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Abstract: A general procedure is described for treating a movable singularity in an integral. This enabĺes us to change the original integral $ {I_0}$ into $ G{I_1}$, where $ G$ depends only on the parameters of the singularity and $ {I_1}$, is a new integral which exists for all values of the parameters. The results are then applied to the particular problem of evaluating

$\displaystyle \int_{ - 1}^1 {\frac{{f(x)dx}} {{{{\{ (1 - {x^2})(1 - {k^2}{x^2})\} }^{1/2}}}}} ,$

where $ f$ is entire and $ k$ varies between 0 and $ 1$. Some new quadrature schemes and new effective methods of evaluating incomplete elliptic integrals are derived.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1970-0275669-4
Keywords: Quadrature, singularities, error, bound
Article copyright: © Copyright 1970 American Mathematical Society