Geodesic
The index ${}_2F_1$-transform of generalized functions
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 4, pp. 657-671 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 ${\bold I} = (0, \infty )$.
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 ${\bold I} = (0, \infty )$.
Classification : 33C90, 44A15, 44A20, 46F12
Keywords: hypergeometric function; index integral transform; generalized functions 
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     author = {Hayek, N. and Gonz\'alez, B. J.},
     title = {The index ${}_2F_1$-transform of generalized functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {657--671},
     year = {1993},
     volume = {34},
     number = {4},
     mrnumber = {1263795},
     zbl = {0793.46019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1993_34_4_a4/}
}
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Hayek, N.; González, B. J. The index ${}_2F_1$-transform of generalized functions. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 4, pp. 657-671. http://geodesic.mathdoc.fr/item/CMUC_1993_34_4_a4/