Integral transforms with generalized Legendre functions as kernels
Compositio Mathematica, Tome 18 (1967) no. 3, p. 235-287
@article{CM_1967__18_3_235_0,
     author = {Braaksma, Boele L. J. and Meulenbeld, B.},
     title = {Integral transforms with generalized Legendre functions as kernels},
     journal = {Compositio Mathematica},
     publisher = {P. Noordhoff N. V., Groningen},
     volume = {18},
     number = {3},
     year = {1967},
     pages = {235-287},
     zbl = {0177.39901},
     mrnumber = {226314},
     language = {en},
     url = {http://www.numdam.org/item/CM_1967__18_3_235_0}
}
Braaksma, B. L. J.; Meulenbeld, B. Integral transforms with generalized Legendre functions as kernels. Compositio Mathematica, Tome 18 (1967) no. 3, pp. 235-287. http://www.numdam.org/item/CM_1967__18_3_235_0/

L. Kuipers and B. Meulenbeld, [1] On a generalization of Legendre's associated differential equation I and II, Proc. Kon. Ned. Ak. v. Wet., Amsterdam 60, 436-450 (1957). | Zbl 0079.09504

B. Meulenbeld, [2] Generalized Legendre's associated functions for real values of the argument numerically less than unity, Proc. Kon. Ned. Ak. v. Wet., Amsterdam 61, 557-563 (1958). | Zbl 0083.05905

N.J. Vilenkin, [3] The matrix elements of irreducible unitary representations of a group of Lobatchevsky space motions and the generalized Fock-Mehler transformations, Dokl. Akad. Nauk S.S.S.R. 118, 219-222 (1958) (Russ.). | MR 104115 | Zbl 0089.25301

F. Götze, [4] Verallgemeinerung einer Integraltransformation von Mehler-Fock durch den von Kuipers und Meulenbeld eingeführten Kern Pm, kn(z), Proc. Kon. Ned. Ak. v. Wet., Amsterdam 68, 396-404 (1965). | Zbl 0141.11304

F.G. Mehler, [5] Über eine mit den Kugel- und Zylinderfunktion verwandte Funktion und ihre Anwendung in der Theorie der Elektrizitätsverteilung, Math. Ann. 18, 161-194 (1881). | JFM 13.0779.02

V.A. Fock, [6] Über die Zerlegung einer willkürlichen Funktion in ein Integral nach Legendreschen Funktionen mit komplexem Index, Dokl. Akad. Nauk S.S.S.R. 39, 279-283 (1943) (Russ.).

E.C. Titchmarsh, [7] Eigenfunction expansions associated with second-order differential equations I, Oxford 1946. | MR 19765 | Zbl 0061.13505

M.N. Olevskiĭ, [8] On the representation of an arbitrary function in the form of an integral with a kernel containing a hypergeometric function, Dokl. Akad. Nauk S.S.S.R. 69, 11-14 (1949) (Russ.). | MR 32832 | Zbl 0038.21602

B. Meulenbeld, [9] New recurrence formulas for the Pmk,n(z) and Qmk,m(z), Monatshefte für Mathematik 64, 355-360 (1960). | Zbl 0094.04003

L. Kuipers and B. Meulenbeld, [10] Related generalized Legendre's associated functions, Arch. Math. 9, 394-400 (1958). | Zbl 0083.05903

G.N. Watson, [11] Asymptotic expansions of hypergeometric functions, Cambridge Phil. Trans. 22, 277-308 (1918).

L. Kuipers and B. Meulenbeld, [12] Linear transformations of generalized Legendre's associated functions, Proc. Kon. Ned. Ak. v. Wet., Amsterdam 61, 330-333 (1958). | Zbl 0083.05904

L. Kuipers, [13] Relations between contiguous generalized Legendre associated functions. Recurrence formulas, Math. Scand. 6, 200-206 (1958). | Zbl 0085.28802

B. Meulenbeld, [14] Wronskians of linearly independent solutions of the generalized Legendre's equation. Recurrence formulas. Math. Nachrichten 21, 193-200 (1960). | Zbl 0095.05302

A. Erdélyia.O., [15] Higher transcendental functions I. New York -Toronto-London, 1953. | Zbl 0051.30303

A. Erdélyia.O., [16] Tables of integral transforms, vol. 2, New York, 1954. | Zbl 0058.34103

B. Meulenbeld et L. Robin, [17] Nouveaux résultats relatifs aux fonctions de Legendre généralisées, Proc. Kon. Ned. Ak. v. Wet., Amsterdam 64, 333-347 (1961). | Zbl 0101.29203