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This is a brief overview of the index hypergeometric transform (other terms for this integral operator are: Olevskii transform, Jacobi transform, generalized Mehler--Fock transform).
Romanovski, V.I. Sur quelques classes nouwels of polynomes orthogonaux
1929
Earlier work this paper cites.
Fock, V. A. On the representation of an arbitrary function by an integral involving Legendre’s functions with a complex index
1943
Earlier work this paper cites.
Titchmarsh E.C. Eigenfunction expansions with second-order differential operators
1946
Earlier work this paper cites.
Olevskiĭ, M. N. On the representation of an arbitrary function in the form of an integral with a kernel containing a hypergeometric function
1949
Earlier work this paper cites.
Erdélyi, A.; Magnus, W.; Oberhettinger, F.; Tricomi, F. G. Higher transcendental functions
1953
Earlier work this paper cites.
Dunford, N., Schwartz, J.T. Linear operators, v.2. Spectral theory. Self adjoint operators in Hilbert space
1963
Earlier work this paper cites.
Wimp, Jet A class of integral transforms
1965
Earlier work this paper cites.
Slater, L. J. Generalized hypergeometric functions
1966
Earlier work this paper cites.
Naimark, M. A. Linear Differential Operators
1968
Earlier work this paper cites.
Vilenkin, N. Ja. Special functions and the theory of group representations
1968
Earlier work this paper cites.
Weyl H. Uber gewonliche lineare Differentialgleichungen mis singularen Stellen und ihre Eigenfunktionen (2 Note)
1968
Earlier work this paper cites.
Macdonald I.G. Spherical functions on groups of p p -adic type
1971
Earlier work this paper cites.
Flensted-Jensen, M., Koornwinder, T. The convolution structure for Jacobi function expansions
1973
Cited alongside, same era.
Koornwinder, T.H., A new proof of a Paley–Wiener theorem for Jacobi transform,
1975
Cited alongside, same era.
Hörmander, L. The analysis of linear partial differential operators.V. 1. Distribution theory and Fourier analysis
1983
Cited alongside, same era.
Koornwinder, T.H., Jacobi functions and analysis on noncompact symmetric spaces
1984
Cited alongside, same era.
Koornwinder, T.H. Special orthogonal polynomial systems mapping to each other by Fourier–Jacobi transform
1985
Cited alongside, same era.
Flensted-Jensen, M., Analysis on non-Riemannian symmetric spaces
1986
Lesky, P. A. Unendliche und endliche Orthogonalsysteme von continuous Hahnpolynomen
1997
Later among the works it cites.
Andrews, G. E., Askey, R., Roy, R. Special functions
1999
Later among the works it cites.
Koelink E., Stockman J.V. Askey–Wilson transform scheme
2001
Later among the works it cites.
Neretin, Yu. A. The index hypergeometric transform and an imitation of the analysis of Berezin kernels on hyperbolic spaces
2001
Later among the works it cites.
Neretin, Yu. A. Beta integrals and finite orthogonal systems of Wilson polynomials
2002
Later among the works it cites.
Cherednik, I.; Ostrik, V. From double Hecke algebra to Fourier transform
2003
Later among the works it cites.
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Cited alongside, same era.
Heckman, G.I., Opdam, E.M., Root systems and hypergeometric functions
1987
Cited alongside, same era.
Molchanov, V.F. The Plancherel formula for pseudo-Riemannian symmetric spaces of rank 1 1
1987
Cited alongside, same era.
Prudnikov, A. P.; Brychkov, Yu. A.; Marichev, O. I. Integrals and series. Vol. 3. More special functions
1990
Cited alongside, same era.
Yakubovich, S.B., Luchko Yu.F., The hypergeometric approach to integral transforms and convolutions
1994
Cited alongside, same era.
Lesky, P. A. Endliche und unendliche Systeme von kontinuierlichen klassischen Orthogonalpolynomen
1996
Cited alongside, same era.
Cherednik I. Harish-Chandra transform and difference operators
1997
Cited alongside, same era.
Groenevelt, W. The Wilson function transform
2003
Later among the works it cites.
Neretin, Yu. A. Some continuous analogues of the expansion in Jacobi polynomials, and vector-valued orthogonal bases
2005
Later among the works it cites.
Neretin, Yu. A. Perturbations of Jacobi polynomials and piece-wise hypergeometric orthogonal systems
2006
Later among the works it cites.
Koekoek, R.; Lesky, P. A.; Swarttouw, R. F. Hypergeometric orthogonal polynomials and their q-analogues
2010
Later among the works it cites.
Neretin Yu.A. Difference Sturm–Liouville problems in the imaginary direction
2012
Closest in time.