Aomoto, K. On the complex Selberg integral. (English) Zbl 0639.33002 Q. J. Math., Oxf. II. Ser. 38, 385-399 (1987). The complex Selberg beta integral is \[ (i/2)\quad n\int_{C\quad n}\prod_{1\leq i<j\leq n}| z_ i-z_ j|^{2\gamma}\prod^{n}_{j=1}| \quad z_ j|^{2\alpha} | z_ j-1|^{2\beta} dz_ j d\bar z_ j. \] This is evaluated as the square of the corresponding Selberg integral times appropriate trigonometric functions. The proof uses contour bending, Hadamard type finite part integrals and some homology as well as the evaluation of Selberg’s beta integral. Reviewer: R.Askey Cited in 20 Documents MSC: 33B15 Gamma, beta and polygamma functions Keywords:complex beta integrals; complex Selberg integral; twisted de Rham cohomology PDFBibTeX XMLCite \textit{K. Aomoto}, Q. J. Math., Oxf. II. Ser. 38, 385--399 (1987; Zbl 0639.33002) Full Text: DOI