Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula

• Autorzy: Hans Weber
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Polynomials with Rodrigues formula; solutions of hypergeometric-type differential equation; generating function in closed form; recursion relations; addition theorem

Kategorie tematyczne

• 35Q40: PDEs in connection with quantum mechanics
• 34B24: Sturm-Liouville theory
• 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
• 42C05: Orthogonal functions and polynomials, general theory

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 2
• Strony: 415-427

Daty

wydano

2007-06-01

online

2007-06-01

Twórcy

autor

Hans Weber

• University of Virginia

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.

Identyfikatory

DOI

10.2478/s11533-007-0004-6