The index ${}_2F_1$-transform of generalized functions

Hayek, N.; González, B. J.

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The index ${}_2F_1$-transform of generalized functions

Hayek, N. ; González, B. J.

Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 4, pp. 657-671.

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Résumé

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 ${\bold I} = (0, \infty )$.

MR Zbl

Classification : 33C90, 44A15, 44A20, 46F12
Keywords: hypergeometric function; index integral transform; generalized functions

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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/