The index \(_ 2 F_ 1\)-transform of generalized functions. (English) Zbl 0793.46019

Hayek Calil, Nácere; González, B. J.

Commentat. Math. Univ. Carol. 34, No. 4, 657-671 (1993).

Summary: The index transformation \[ F(\tau)=\int^ \infty_ 0 f(t){_ 2 F_ 1}(\mu+\textstyle{{1\over 2}}+ i\tau,\;\mu+\textstyle{{1\over 2}}- i\tau;\;\mu+1; -t)t^ \alpha dt, \] \({_ 2F_ 1}(\mu+{1\over 2}+ i\tau, \mu+{1\over 2}-i\tau; \mu+1; -t)\) being the Gauss hypergeometric function, is defined on certain space of generalized functions and its inversion formula established for distributions of compact support on \(I=(0,\infty)\).

MSC:

46F12

Integral transforms in distribution spaces

Keywords:

index integral transform; Gauss hypergeometric function; space of generalized functions; inversion formula; distributions of compact support