
In 1944 A. Selberg evaluated a multivariable beta integral known as Selberg's beta integral. In [SIAM J. Math. Anal. 11, 938-951 (1980; Zbl 0458.33002)] \textit{R. A. Askey} conjectured a number of \(q\)-extensions of this integral based upon various \(q\)-beta integrals. One of these conjectured \(q\)-integrals was proved by the author in [SIAM J. Math. Anal. 19, No. 4, 969-986 (1988; Zbl 0643.33004)] and by \textit{L. Habsieger} [SIAM J. Math. Anal. 19, No. 6, 1475-1489 (1988; Zbl 0664.33001)]. In this paper the author proves an Aomoto-type extension of an other conjectured Selberg \(q\)-beta integral. Part of the proof is based on an argument by \textit{M. E. H. Ismail} [Proc. Am. Math. Soc. 63, 185-186 (1977; Zbl 0351.33002)]. The result generalizes Askey's last conjectured Selberg \(q\)-beta integral which was proved by \textit{R. J. Evans} in [Contemp. Math. 166, 341-357 (1994; Zbl 0820.33001)]. Other extensions of Selberg's beta integral were obtained and proved by \textit{R. A. Gustafson} in [Bull. Am. Math. Soc. 22, No. 1, 97-105 (1990; Zbl 0693.33001); SIAM J. Math. Anal. 23, No. 2, 525-551 (1992; Zbl 0764.33008)].
Aomoto-type extensions, Selberg's integral, Applied Mathematics, Other basic hypergeometric functions and integrals in several variables, Selberg \(q\)-integrals, q-transportation theory for the root system An−1, Aomoto-type extension, Analysis
Aomoto-type extensions, Selberg's integral, Applied Mathematics, Other basic hypergeometric functions and integrals in several variables, Selberg \(q\)-integrals, q-transportation theory for the root system An−1, Aomoto-type extension, Analysis
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