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Keywords:
hypergeometric function; index integral transform; generalized functions
hypergeometric function; index integral transform; generalized functions
Summary:
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 ${\bold I} = (0, \infty )$.
References:
[1] Erdelyi A., Magnus W., Oberhettinger F., Tricomi F.: Higher Transcendental Functions. vol. I, McGraw-Hill Book Co. Inc., New York, 1953. Zbl 0064.06302
[2] Erdelyi A., Magnus W., Oberhettinger F., Tricomi F.: Tables of Integral Transforms. vol. II, McGraw-Hill Book Co. Inc., New York, 1954. MR 0065685 | Zbl 0184.33704
[3] Glaeske H.N., Hess A.: On the Convolution Theorem of the Mehler-Fock-Transform for a Class of Generalized Functions (II). Math. Nachr. (1988), 119-129. MR 0952467 | Zbl 0649.46037
[4] Hayek N.: Estudio de la ecuación diferencial $xy'' + (\nu + 1)y' + y = 0$ y de sus aplicaciones. Collect. Mat. XVII (1966-67), 57-174. MR 0224876
[5] Hayek N.: Sobre la transformación de Hankel. Actas de la VIII Reunión Anual de Matemáticos Espa noles, Madrid, 1968, pp. 47-60. MR 0420164
[6] Hayek N., Negrin E.R., Gonzalez B.J.: Una clase de transformada índice relacionada con la de Olevskii. Actas XIV Jornadas Hispano-Lusas de Matemáticas (Puerto de la Cruz), vol. I, 1989, pp. 401-405. MR 1112907
[7] Lebedev N.N.: Sur une formule d'inversion. Dokl. Akad. Nauk. SSSR 52 (1946), 655-658. MR 0021144
[8] Mendez J.M.: La transformación integral de Hankel-Clifford. Tesis, Secretariado de Publicaciones, Univ. La Laguna, Col. Monog. N. 8, 1981.
[9] Olver F.W.J.: Asymptotics and special functions. Academic Press, New York, 1967. MR 0435697 | Zbl 0982.41018
[10] Robin L.: Fonctions Sphériques de Legendre et Fonctions Sphéroidales, Tome II. GauthierVillars, Paris, 1958. MR 0101928 | Zbl 0088.05102
[11] Schwartz L.: Théorie des distributions. Hermann & Cie., Paris, 1966. MR 0209834 | Zbl 0962.46025
[12] Van Der Pol B., Bremer H.: Operational Calculus. Cambridge University Press, New York, 1964.
[13] Vu Kim Tuan, Marichev O.I., Yakubovich S.B.: Composition structure of integral transformations. Sov. Math. Dokl. 33 (1986), 166-170. Zbl 0604.44003
[14] Zemanian A.H.: Generalized integral transformations. Interscience Publishers, New York, 1968. MR 0423007 | Zbl 0643.46029
[15] Zemanian A.H.: The Kantorovich-Lebedev transformation on distributions of compact support and its inversion. Math. Proc. Camb. Philos. Soc. 77 (1975), 139-143. MR 0355489
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