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Mathematics of Computation

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



Integrals of Jacobi functions

Authors: Shyam L. Kalla, Salvador Conde and Yudell L. Luke
Journal: Math. Comp. 38 (1982), 207-214
MSC: Primary 33A25; Secondary 33-04, 65D30
MathSciNet review: 637298
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Abstract: In this paper, we study $\smallint _{ - 1}^1{(1 - x)^a}{(1 + x)^b}P_\nu ^{(\alpha ,\beta )}(x) dx$ and its partial derivatives with respect to a and b, where $P_\nu ^{(\alpha ,\beta )}(x)$ is the Jacobi function. Our expressions generalize the work of Blue, Gautschi and Gatteschi. The results are useful to derive integration formulas for integrands with algebraic and logarithmic singularities.

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Article copyright: © Copyright 1982 American Mathematical Society