Abstract:In this paper the index transformation $$ F(\tau ) = \int _{0}^{\infty } f(t) {}_{2}F_{1}( \mu + \frac {1}{2} + i \tau , \mu + \frac {1}{2} - i \tau ; \mu + 1; -t ) t^{\alpha } dt $$ ${}_{2}F_{1}( \mu + \frac {1}{2} + i \tau , \mu + \frac {1}{2} - i \tau ; \mu + 1; -t ) $ being the Gauss hypergeometric function, is defined on certain space of generalized functions and its inversion formula established for distributions of compact support on ${\bold I} = (0, \infty )$.
Keywords: hypergeometric function, index integral transform, generalized functions
AMS Subject Classification: 44A15, 46F12