Book chapter
Numerical Quadrature
Spherical Harmonics and Approximations on the Unit Sphere: An Introduction, pp.165-210
Lecture Notes in Mathematics, Springer Berlin Heidelberg
01/10/2012
DOI: 10.1007/978-3-642-25983-8_5
Abstract
In this chapter we discuss numerical approximation of the integral 5.1\documentclass[12pt]{minimal}
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\begin{document}
$$\begin{array}{rcl} I(f) ={ \int \nolimits \nolimits }_{{\mathbb{S}}^{2}}f(\eta )\,d{S}^{2}(\eta ).& &\end{array}$$
\end{document}The integrand fcan be well-behaved or singular, although our initial development assumes fis continuous and, usually, several times continuously differentiable. Such integrals occur in a wide variety of physical applications; and the calculation of the coefficients in a Laplace series expansion of a given function (see (4.55)) requires evaluating such integrals.
Details
- Title: Subtitle
- Numerical Quadrature
- Creators
- Kendall AtkinsonWeimin Han
- Resource Type
- Book chapter
- Publication Details
- Spherical Harmonics and Approximations on the Unit Sphere: An Introduction, pp.165-210
- Series
- Lecture Notes in Mathematics
- DOI
- 10.1007/978-3-642-25983-8_5
- eISSN
- 1617-9692
- ISSN
- 0075-8434
- Publisher
- Springer Berlin Heidelberg; Berlin, Heidelberg
- Language
- English
- Date published
- 01/10/2012
- Academic Unit
- Computer Science; Mathematics
- Record Identifier
- 9984240879302771
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