Throughout this subsection we assume ; sometimes however, this restriction can be eased by analytic continuation.
For the Bessel function see §10.2(ii).
For the generalized hypergeometric function see (16.2.1).
These integrals are Cauchy principal values (§1.4(v)).
The case is a limit case of an integral for Jacobi polynomials; see Askey and Razban (1972).
provided that is even and the sum of any two of is not less than the third; otherwise the integral is zero.
For further integrals, see Apelblat (1983, pp. 189–204), Erdélyi et al. (1954a, pp. 38–39, 94–95, 170–176, 259–261, 324), Erdélyi et al. (1954b, pp. 42–44, 271–294), Gradshteyn and Ryzhik (2000, pp. 788–806), Gröbner and Hofreiter (1950, pp. 23–30), Marichev (1983, pp. 216–247), Oberhettinger (1972, pp. 64–67), Oberhettinger (1974, pp. 83–92), Oberhettinger (1990, pp. 44–47 and 152–154), Oberhettinger and Badii (1973, pp. 103–112), Prudnikov et al. (1986b, pp. 420–617), Prudnikov et al. (1992a, pp. 419–476), and Prudnikov et al. (1992b, pp. 280–308).