Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Movable singularities and quadrature

Authors: R. F. Goodrich and F. Stenger
Journal: Math. Comp. 24 (1970), 283-300
MSC: Primary 65.55
MathSciNet review: 0275669
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.55

Retrieve articles in all journals with MSC: 65.55

Additional Information

Keywords: Quadrature, singularities, error, bound
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society