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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.

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

  • [1] W. N. Bailey, Generalized Hypergeometric Series, Cambridge Univ. Press, Cambridge, 1935.
  • [2] J. L. Blue, ``A Legendre polynomial integral,'' Math. Comp., v. 33, 1979, pp. 739-741. MR 521287 (81b:65021a)
  • [3] L. Gatteschi, ``On some orthogonal polynomial integrals,'' Math. Comp., v. 35, 1980, pp. 1291-1298. MR 583506 (81h:33015)
  • [4] W. Gautschi, ``On the preceding paper 'A Legendre polynomial integral' by James L. Blue,'' Math. Comp., v. 33, 1979, pp. 742-743. MR 521288 (81b:65021b)
  • [5] Y. L. Luke, The Special Functions and Their Approximations, Vols. 1, 2, Academic Press, New York, 1969.
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  • [7] L. J. Slater, Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966. MR 0201688 (34:1570)

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Article copyright: © Copyright 1982 American Mathematical Society

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