Classical symmetric orthogonal polynomials of a discrete variable

Classification of polynomial solutions of second-order difference equation of hypergeometric type with real coefficients, orthogonal with respect to a positive symmetric weight function is presented.

[1]  M. N. Hounkonnou,et al.  The transformation of polynomial eigenfunctions of linear second-order difference operators: a special case of Meixner polynomials , 2001 .

[2]  Discrete Darboux transformation for discrete polynomials of hypergeometric type , 1998, math/9805142.

[3]  V. B. Uvarov,et al.  Classical Orthogonal Polynomials of a Discrete Variable , 1991 .

[4]  K. Wolf,et al.  Fractional Fourier-Kravchuk transform , 1997 .

[5]  Iván Area,et al.  Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: discrete case , 1997 .

[6]  R. Askey,et al.  A Set of Hypergeometric Orthogonal Polynomials , 1982 .

[7]  Begnaud Francis Hildebrand,et al.  Introduction to numerical analysis: 2nd edition , 1987 .

[8]  Arnold Neumaier,et al.  Introduction to Numerical Analysis , 2001 .

[9]  Rene F. Swarttouw,et al.  The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue Report Fac , 1996, math/9602214.

[10]  Eduardo Godoy,et al.  Recurrence relations for connection coefficients between two families of orthogonal polynomials , 1995 .

[11]  K. Wolf,et al.  Approximation on a finite set of points through kravchuk functions , 1993 .

[12]  M. Lorente.  Raising and lowering operators, factorization and differential/difference operators of hypergeometric type , 2001 .

[13]  M. Anshelevich,et al.  Introduction to orthogonal polynomials , 2003 .

[14]  K. B. Oldham,et al.  An Atlas of Functions. , 1988 .

[15]  K. Wolf,et al.  The canonical Kravchuk basis for discrete quantum mechanics , 2000 .

[16]  K. Wolf,et al.  Continuous vs. discrete fractional Fourier transforms , 1999 .