A \(_1\Psi_1\) summation theorem for Macdonald polynomials (Q1273313)

The function introduced is an \(n\)-dimensional series whose terms involve Macdonald polynomials corresponding to partitions of length at most \(n\), and suitably generalized factorials. The definition is too long to reproduce here. So also is the main result, which is reminiscent of Ramanujan's \(_1\psi_1\) summation theorem, and the two corollaries: A \(q\)-integral formula of Selberg type, and the triple product identity for Macdonald polynomials given by the author [J. Math. Anal. Appl. 200, No. 2, 355-367 (1996; Zbl 0855.33010)].