Computing the Hilbert transform of a Jacobi weight function |
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Authors: | Walter Gautschi Jet Wimp |
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Institution: | (1) Department of Computer Sciences, Purdue University, 47907 West Lafayette, Indiana, U.S.A. |
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Abstract: | We discuss the evaluation of the Hilbert transformf
–1
1
(t-)–1
w(, )(t)dt,–1<<1, of the Jacobi weight functionw(, )(t)=(1–t))(1+t) by analytic and numerical means and also comment on the recursive computation of the quantitiesf
–1
1
)(t–)–1
n
(t;w
(, ))
w
(, )(t)dt,n=0, 1, 2, ..., where
n
(·;w
(, )) is the Jacobi polynomial of degreen.The work of the first author was supported in part by the National Science Foundation under grant DCR-8320561. The work of the second author was supported by the National Science Foundation under grant DMS-8419086. |
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Keywords: | 65D30 65D32 65R10 |
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