Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Numerical quadrature rules for some infinite range integrals

Author: Avram Sidi
Journal: Math. Comp. 38 (1982), 127-142
MSC: Primary 65D32
MathSciNet review: 637291
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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 $ \smallint _0^\infty {x^\alpha }{e^{ - x}}f(x)\,dx$ and $ \smallint _0^\infty {x^\alpha }{E_p}(x)f(x)\,dx$, where $ {E_p}(x)$ is the exponential integral. It turns out the new rules are of interpolatory type, their abscissas are distinct and lie in the interval of integration and their weights, at least numerically, are positive. For fixed $ \alpha $ 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 $ \smallint _{ - \infty }^{ + \infty }\vert x{\vert^\beta }{e^{ - {x^2}}}f(x)\,dx$ too are considered.

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

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D32

Retrieve articles in all journals with MSC: 65D32

Additional Information

PII: S 0025-5718(1982)0637291-5
Article copyright: © Copyright 1982 American Mathematical Society