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

DOI:
https://doi.org/10.1090/S0025-5718-1982-0637298-8

MathSciNet review:
637298

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Abstract: In this paper, we study and its partial derivatives with respect to *a* and *b*, where 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.

**[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.**[6]**Y. L. Luke,*Mathematical Functions and Their Approximations*, Academic Press, New York, 1975. MR**0501762 (58:19039)****[7]**L. J. Slater,*Generalized Hypergeometric Functions*, Cambridge Univ. Press, Cambridge, 1966. MR**0201688 (34:1570)**

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DOI:
https://doi.org/10.1090/S0025-5718-1982-0637298-8

Article copyright:
© Copyright 1982
American Mathematical Society