Hyperbolic Beta Integrals

  title={Hyperbolic Beta Integrals},
  author={Jasper V. Stokman},
Hyperbolic beta integrals are analogues of Euler’s beta integral in which the role of Euler’s gamma function is taken over by Ruijsenaars’ hyperbolic gamma function. They may be viewed as (q, q̃ )-bibasic analogues of the beta integral in which the two bases q and q̃ are interrelated by modular inversion, and they entail q-analogues of the beta integral for |q| = 1. The integrals under consideration are the hyperbolic analogues of the Ramanujan integral, the Askey-Wilson integral and the… CONTINUE READING