| Affiliation: | (1) St. Petersburg Branch of Steklov Mathematical Institute, Fontanka 27, St Petersburg, 191023, Russia;(2) Department of Mathematical Sciences, Indiana University Purdue University at Indianpolis, Indianapolis, IN 46202-3216, USA;(3) Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA |
| Abstract: | Given complex numbers m1, I1 and nonnegative integers m2, I2, such that m1+m2 = I1+ I2, we define I2-dimensional hypergeometric integrals Ia,b(z; m1, m2, I1, I2), a,b = 0,. . . ,min)(m2,I2), depending on a complex parameter z. We show that Ia,b(z;m1, m2,I1, I2) = Ia,b(z;I1, I2,m1,m2), thus establishing an equality of I2 and m2-dimensional integrals. This identity allows us to study asymptotics of the integrals with respect to their dimension in some examples. The identity is based on the ( k,  k,) duality for the KZ and dynamical differential equations.Mathematics Subject Classifications (2000). 33C70, 33C80, 81R10 |
