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Finite summation formulas and congruences for Legendre and Jacobi polynomials. (English) Zbl 0087.03704

number theory
Full Text: DOI EuDML
[1] W. A. Al-Salam andL. Carlitz, Some finite summation formulas for the classical orthogonal polynomials, Rendiconti di Matematica, vol. 16 91957),
[2] W. A. Al-Salam andL. Carlitz, Congruence properties of the classical orthogonal polynomials, Duke Mathematical Journal, vol. 25 (1958).
[3] P. Appell andJ. Kampe de Ferriet, Fonctions hypergéometrique et hypersphérique. Polynomes d’Hermite, Paris 1926.
[4] H. Bateman, A generalization of the Legendre polynomial, Proceedings of the London Mathematical Society, (2), vol 3 (1905), pp. 111-123. · Zbl 36.0512.01 · doi:10.1112/plms/s2-3.1.111
[5] E. Catalan, Novelles propriétés des fonctionX n , Mémoire de l’Académie Royale des sciences, des lettres, et des beaux-arts de Belgique, vol. 47 (1889).
[6] I. J. Good, A new finite series for the Legendre polynomials, Proceedings of the Cambridge Philosophical Society, vol. 51 (1955) part 2, pp. 385-388. · Zbl 0065.05701 · doi:10.1017/S0305004100030334
[7] G. Pólya andG. Szegö, Aufgaben und Lehrsätze aus der Analysis, vol. 2, Berlin 1954.