The index 2 F 1 -transform of generalized functions

N. Hayek; Benito J. González

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 4, page 657-671
  • ISSN: 0010-2628

Abstract

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In this paper the index transformation F ( τ ) = 0 f ( t ) 2 F 1 ( μ + 1 2 + i τ , μ + 1 2 - i τ ; μ + 1 ; - t ) t α d t 2 F 1 ( μ + 1 2 + i τ , μ + 1 2 - i τ ; μ + 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 , ) .

How to cite

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Hayek, N., and González, Benito J.. "The index ${}_2F_1$-transform of generalized functions." Commentationes Mathematicae Universitatis Carolinae 34.4 (1993): 657-671. <http://eudml.org/doc/247470>.

@article{Hayek1993,
abstract = {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 $\{\mathbf \{I\}\} = (0, \infty )$.},
author = {Hayek, N., González, Benito J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {hypergeometric function; index integral transform; generalized functions; index integral transform; Gauss hypergeometric function; space of generalized functions; inversion formula; distributions of compact support},
language = {eng},
number = {4},
pages = {657-671},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The index $\{\}_2F_1$-transform of generalized functions},
url = {http://eudml.org/doc/247470},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Hayek, N.
AU - González, Benito J.
TI - The index ${}_2F_1$-transform of generalized functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 4
SP - 657
EP - 671
AB - 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 ${\mathbf {I}} = (0, \infty )$.
LA - eng
KW - hypergeometric function; index integral transform; generalized functions; index integral transform; Gauss hypergeometric function; space of generalized functions; inversion formula; distributions of compact support
UR - http://eudml.org/doc/247470
ER -

References

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  14. Zemanian A.H., Generalized integral transformations, Interscience Publishers, New York, 1968. Zbl0643.46029MR0423007
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