Identities for Hypergeometric Integrals of Different Dimensions
نویسندگان
چکیده
منابع مشابه
Recurrences for elliptic hypergeometric integrals
In recent work on multivariate elliptic hypergeometric integrals, the author generalized a conjectural integral formula of van Diejen and Spiridonov to a ten parameter integral provably invariant under an action of the Weyl group E7. In the present note, we consider the action of the affine Weyl group, or more precisely, the recurrences satisfied by special cases of the integral. These are of t...
متن کاملTheta Hypergeometric Integrals
A general class of (multiple) hypergeometric type integrals associated with the Jacobi theta functions is defined. These integrals are related to theta hypergeometric series via the residue calculus. In the one variable case, theta function extensions of the Meijer function are obtained. A number of multiple generalizations of the elliptic beta integral associated with the root systems An and C...
متن کاملLimits of elliptic hypergeometric integrals
In [16], the author proved a number of multivariate elliptic hypergeometric integrals. The purpose of the present note is to explore more carefully the various limiting cases (hyperbolic, trigonometric, rational, and classical) that exist. In particular, we show (using some new estimates of generalized gamma functions) that the hyperbolic integrals (previously treated as purely formal limits) a...
متن کاملTransformations of elliptic hypergeometric integrals
We prove a pair of transformations relating elliptic hypergeometric integrals of different dimensions, corresponding to the root systems BCn and An; as a special case, we recover some integral identities conjectured by van Diejen and Spiridonov. For BCn, we also consider their “Type II” integral. Their proof of that integral, together with our transformation, gives rise to pairs of adjoint inte...
متن کاملTransformations of hypergeometric elliptic integrals
The paper classifies algebraic transformations of Gauss hypergeometric functions with the local exponent differences (1/2, 1/4, 1/4), (1/2, 1/3, 1/6) and (1/3, 1/3, 1/3). These form a special class of algebraic transformations of Gauss hypergeometric functions, of arbitrary high degree. The Gauss hypergeometric functions can be identified as elliptic integrals on the genus 1 curves y = x − x or...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 2005
ISSN: 0377-9017,1573-0530
DOI: 10.1007/s11005-004-6364-y