Geodesic
The index ${}_2F_1$-transform of generalized functions
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 4, pp. 657-671

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{CMUC_1993__34_4_a4,
     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},
     publisher = {mathdoc},
     volume = {34},
     number = {4},
     year = {1993},
     mrnumber = {1263795},
     zbl = {0793.46019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1993__34_4_a4/}
}
TY  - JOUR
AU  - Hayek, N.
AU  - González, B. J.
TI  - The index ${}_2F_1$-transform of generalized functions
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1993
SP  - 657
EP  - 671
VL  - 34
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_1993__34_4_a4/
LA  - en
ID  - CMUC_1993__34_4_a4
ER  - 
%0 Journal Article
%A Hayek, N.
%A González, B. J.
%T The index ${}_2F_1$-transform of generalized functions
%J Commentationes Mathematicae Universitatis Carolinae
%D 1993
%P 657-671
%V 34
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_1993__34_4_a4/
%G en
%F CMUC_1993__34_4_a4
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/