Hahn polynomial

The Hahn polynomials are a set of orthogonal polynomials in the Askey scheme . They were introduced by Tschebyscheff in 1875 and rediscovered by Wolfgang Hahn in 1949 .

definition

The Hahn polynomials can be defined using the hypergeometric function as follows: ${\displaystyle Q_{n}}$ ${\displaystyle {}_{3}F_{2}}$

${\displaystyle Q_{n}(x;\alpha ,\beta ,N):={}_{3}F_{2}(-n,-x,n+\alpha +\beta +1;\alpha +1,-N+1;1)\,.}$

credentials

• Eric W. Weisstein : Hahn Polynomial . In: MathWorld (English).
• Chebyshev, P. (1907), "Sur l'interpolation des valeurs equidistantes" , in Markoff, A .; Sonin, N., Oeuvres de PL Tchebychef, 2, pp. 219-242
• Hahn, Wolfgang (1949), "About orthogonal polynomials that satisfy q-difference equations", Mathematische Nachrichten 2: 4–34 doi : 10.1002 / mana.19490020103
• Koekoek, Roelof; Lesky, Peter A .; Swarttouw, René F. (2010), Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics, Berlin, New York: Springer-Verlag , ISBN 978-3-642-05013-8 , doi : 10.1007 / 978-3 -642-05014-5
• Koornwinder, Tom H .; Wong, Roderick SC; Koekoek, Roelof; Swarttouw, René F. (2010), "Hahn Class: Definitions" , in Olver, Frank WJ; Lozier, Daniel M .; Boisvert, Ronald F. et al., NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0521192255