The index ${}_2F_1$-transform of generalized functions
Hayek, N. ; González, Benito J.
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993), p. 657-671 / Harvested from 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 ${\bold I} = (0, \infty )$.

Publié le : 1993-01-01
Classification:  33C90,  44A15,  44A20,  46F12 
@article{118623,
     author = {N. Hayek and Benito J. Gonz\'alez},
     title = {The index ${}\_2F\_1$-transform of generalized functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {34},
     year = {1993},
     pages = {657-671},
     zbl = {0793.46019},
     mrnumber = {1263795},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118623}
}

Hayek, N.; González, Benito J. The index ${}_2F_1$-transform of generalized functions. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 657-671. http://gdmltest.u-ga.fr/item/118623/

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