On some generalized symmetric integral operators of Buschman-Erdelyi’s type. (English) Zbl 0949.44003
Summary: Some new symmetric integral operators with kernels involving generalized Legendre functions of the first kind \(P_k^{m,n}(z)\) are introduced. Some of their applications are given.
MSC:
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
| 33C90 | Applications of hypergeometric functions |
References:
| [1] | Samko S., Kilbas A., Marichev O., Integrals and Derivatives of Fractional Order and Some its Applications, Minsk, 1987, 688p. (in Russian). · Zbl 0617.26004 |
| [2] | Gupta K.C., Mittal P.K., The H-function transform, J. of Austr. Math. Soc, 1970, V.11, 2, 142-148. · Zbl 0193.08401 |
| [3] | Rooney P.G., On integral transformations with G-function kernels, Proc. Royal Soc. of Edinburgh A, 1983, V.93, N 3-4, 181-188. · Zbl 0509.44001 |
| [4] | Buschman R.G., An inversion integral for a general Legendre transformation, SIAM Rev., 1963, N 3, 232-233. · Zbl 0115.32703 |
| [5] | Erdelyi, A., An integral equations involving Legendre functions, Soc. Industr. and Appl. Math., 12, 1, 15-30, 1964 · Zbl 0178.14401 |
| [6] | Copson E.T., On a singular boundary value problem for an equation of hyperbolic type, Arct. Ration. Mech. and Anal, 1958, V.1, N4, 349-356. · Zbl 0081.08902 |
| [7] | Lulwig, D., The Radon transform on Euclidian Space, Comm. on Pure and Appl., 19, 49-81, 1966 · Zbl 0134.11305 |
| [8] | Muller C., Richberg R. Über die Radon transformation, Math. Meth. Appl. Sci., 1960, 106-109. |
| [9] | Katrachov V., Singular boundary value problems and the operators of transformation, In: The correct boundary value problems for non-classic equations of math. physics, Novosibirsk, 1981, 87-91 (in Russian). · Zbl 0508.47050 |
| [10] | Kuipers L., Meulenbeld B., On a generalization of Legendre’s associated differential equation I,II, Proc. Kon. Ned. Ak. v. W., Ser. A, 1957, V.60, N 4. 337-350. · Zbl 0079.09504 |
| [11] | Virchenko N., On some applications of the generalized associated Legendre’s functions, Ukr. math. J., 1987, V.39, N 2, 149-156 (in Russian). · Zbl 0618.33006 |
| [12] | Watson H., The Theory of Bessel function, Moscow, 1949, I, 793p. · JFM 01.0159.05 |
| [13] | Bateman H., Erdelyi A., The Tables of Integral Transforms, Moscow, 1969, I, 344p. · Zbl 0146.09301 |
| [14] | Bateman H., Erdelyi A., Higher Transcendental Functions, Moscow, 1965, I, 296p. · Zbl 0143.29202 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
