nLab
elliptic Selberg integral

analytic integration	cohomological integration
measurable space	Poincaré duality
measure	orientation in generalized cohomology
volume form	(virtual) fundamental class
Riemann/Lebesgue integration of differential forms	push-forward in generalized cohomology/in differential cohomology

Analytic integration

J.F. van Diejen, V.P. Spiridonov, An elliptic Macdonald-Morris conjecture and multiple modular hypergeometric sums, Math. Res. Letters 7 (2000) 729–746; Elliptic Selberg integrals, Internat. Math. Res. Notices 20, (2001), 1083–1110; Modular hypergeometric residue sums of elliptic Selberg integrals, Lett. Math. Phys. 58 (2001), 223–238.
G. Felder, L. Stevens, A. Varchenko, Elliptic Selberg integrals and conformal blocks, Math. Res. Lett. 10 (2003), no. 5-6, 671–684, MR2004i:32024, pdf
V. P. Spiridonov, Elliptic beta integrals and solvable models of statistical mechanics, arxiv/1011.3798

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