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2007 | 5 | 2 | 415-427
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Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula

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Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas. Applications to the classical polynomials are given.
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Bibliografia
  • [1] A.F. Nikiforov and V.B. Uvarov: Special Functions of Mathematical Physics, Birkhäuser Verlag, Basilea, 1988.
  • [2] M.E.H. Ismail: Classical and Quantum Orthogonal Polynomials in One Variable, Cambridge Univ. Press, Cambridge, 2005.
  • [3] P.A. Lesky: “Endliche und unendliche Systeme von kontinuierlichen klassischen Orthogonalpoynomen”, Z. Angew. Math. Mech., Vol. 76(3), (1996), pp. 181–184.
  • [4] G. Szegö: Orthogonal Polynomials, Vol. XXIII, American Math. Soc., Providence, RI, 1939.
  • [5] G.B. Arfken and H.J. Weber: Mathematical Methods for Physicists, 6th ed., Elsevier-Academic Press, Amsterdam, 2005.
  • [6] P. Dennery and A. Krzywicki: Mathematics for Physicists, Dover, New York, 1996.
  • [7] M. Abramowitz and I.A. Stegun: Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover, 2nd edition, New York, 1972.
  • [8] I.S. Gradshteyn and I.M. Ryzhik: Table of Integrals, Series and Products, ed. A. Jeffrey, Acad. Press, San Diego, 2000.
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bwmeta1.element.doi-10_2478_s11533-007-0004-6
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