Integral transforms with generalized Legendre functions as kernels

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1. L. Kuipers and B. Meulenbeld, [1] On a generalization of Legendre's associated differential equation I and II, Proc. Kon. Ned. Ak. v. Wet., Amsterdam60, 436—450 (1957). Zbl0079.09504
2. B. Meulenbeld, [2] Generalized Legendre's associated functions for real values of the argument numerically less than unity, Proc. Kon. Ned. Ak. v. Wet., Amsterdam61, 557—563 (1958). Zbl0083.05905
3. 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.). Zbl0089.25301MR104115
4. 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., Amsterdam68, 396—404 (1965). Zbl0141.11304
5. 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). Zbl13.0779.02JFM13.0779.02
6. 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.). 
7. E.C. Titchmarsh, [7] Eigenfunction expansions associated with second-order differential equations I, Oxford1946. Zbl0061.13505MR19765
8. 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.). Zbl0038.21602MR32832
9. B. Meulenbeld, [9] New recurrence formulas for the Pmk,n(z) and Qmk,m(z), Monatshefte für Mathematik64, 355—360 (1960). Zbl0094.04003
10. L. Kuipers and B. Meulenbeld, [10] Related generalized Legendre's associated functions, Arch. Math.9, 394—400 (1958). Zbl0083.05903
11. G.N. Watson, [11] Asymptotic expansions of hypergeometric functions, Cambridge Phil. Trans.22, 277—308 (1918). 
12. L. Kuipers and B. Meulenbeld, [12] Linear transformations of generalized Legendre's associated functions, Proc. Kon. Ned. Ak. v. Wet., Amsterdam61, 330—333 (1958). Zbl0083.05904
13. L. Kuipers, [13] Relations between contiguous generalized Legendre associated functions. Recurrence formulas, Math. Scand.6, 200—206 (1958). Zbl0085.28802
14. B. Meulenbeld, [14] Wronskians of linearly independent solutions of the generalized Legendre's equation. Recurrence formulas. Math. Nachrichten21, 193—200 (1960). Zbl0095.05302
15. A. Erdélyia.o., [15] Higher transcendental functions I. New York -Toronto-London, 1953. Zbl0051.30303
16. A. Erdélyia.o., [16] Tables of integral transforms, vol. 2, New York, 1954. Zbl0058.34103
17. B. Meulenbeld et L. Robin, [17] Nouveaux résultats relatifs aux fonctions de Legendre généralisées, Proc. Kon. Ned. Ak. v. Wet., Amsterdam64, 333—347 (1961). Zbl0101.29203