Selberg-Jack character sums of dimension 2 (Q1900859)

\textit{K. W. J. Kadell} [ Adv. Math. 130, No. 1, 33-102 (1997)] extended Selberg's \(n\)-dimensional beta integral formula by inserting a normalized Jack polynomial as a factor in the integrand. In this paper the author formulates and proves a character sum analog of Kadell's formula in the case \(n=2\), raising hope that such an analog may exist for general \(n\). In 1981 the author studied character sum analogs of Selberg's integral formula and limiting cases for general \(n\) that have been proved by him in 1991 using G. Anderson's work.