Integrals of Jacobi functions

Kalla, Shyam L.; Conde, Salvador; Luke, Yudell L.

doi:10.1090/S0025-5718-1982-0637298-8

Integrals of Jacobi functions
HTML articles powered by AMS MathViewer

by Shyam L. Kalla, Salvador Conde and Yudell L. Luke PDF

Math. Comp. 38 (1982), 207-214 Request permission

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

Generalized Hypergeometric Series

James L. Blue, A Legendre polynomial integral, Math. Comp. 33 (1979), no. 146, 739–741. MR 521287, DOI 10.1090/S0025-5718-1979-0521287-8
Luigi Gatteschi, On some orthogonal polynomial integrals, Math. Comp. 35 (1980), no. 152, 1291–1298. MR 583506, DOI 10.1090/S0025-5718-1980-0583506-X
James L. Blue, A Legendre polynomial integral, Math. Comp. 33 (1979), no. 146, 739–741. MR 521287, DOI 10.1090/S0025-5718-1979-0521287-8

The Special Functions and Their Approximations

Yudell L. Luke, Mathematical functions and their approximations, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0501762
Lucy Joan Slater, Generalized hypergeometric functions, Cambridge University Press, Cambridge, 1966. MR 0201688