Hypergeometric Orthogonal Polynomials

By R. Koekoek, P. Lesky, Rene F. Swarttouw. 2010

1,140 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/4c450d5c8d01fb0cb118cc947556efcd54adf4b9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Paul M. Terwilliger
2. Alexei S. Zhedanov
3. Luc Vinet
4. Eid H. Doha
5. Dumitru Băleanu
6. Antonio J. Dur'an
7. Satoshi Tsujimoto
8. Thabet Abdeljawad

In Computational Theory and Mathematics

1. Alexei S. Zhedanov
2. Luc Vinet
3. Eid H. Doha
4. Lauren K. Williams
5. Dumitru Băleanu
6. Paul M. Terwilliger
7. Antonio J. Dur'an
8. Satoshi Tsujimoto

Citations in the corpus

• The Universal Askey-Wilson Algebra (2011, background): “These polynomials are the most general family in a master class of orthogonal polynomials called the Askey scheme [37].”
• Tableaux combinatorics for the asymmetric exclusion process and Askey-Wilson polynomials (2009, background): “They reside at the top of the hierarchy of the one-variable orthogonal polynomial family in the Askey scheme [2, 25, 32].”
• Spectral technique for solving variable‐order fractional Volterra integro‐differential equations (2018, background): “2 The properties of the shifted Legendre polynomials We recall that the Legendre polynomials [57] Pk(t)(k = 0, 1, 2, .”
• A ‘missing’ family of classical orthogonal polynomials (2010, methodology): “The Askey scheme [17, 18] provides a list of all known ‘classical’ orthogonal polynomials.”
• A LIMIT q = −1 FOR THE BIG Q-JACOBI POLYNOMIALS (2012, background): “…satisfy the eigenvalue equation [10], [11] (2.4) where the operator L is The orthogonality relation is with the q -integral defined as [10], [11] and the weight function where ( a ; q ) s = (1 − a )(1 − aq ) . . . (1 − aq s − 1 ) is the shifted q -factorial [11] and ( a ; q ) ∞ = lim s →∞ (…”
• Towards a full solution of the large N double-scaled SYK model (2018, neutral): “To give some perspective on orthogonal polynomials encountered in this paper, there is a convenient pattern called q-Askey scheme.[59] It can be thought of as a ‘map’ of frequently used hypergeometric orthogonal polynomials, modelled on a certain four-dimensional manifold having boundaries and corne”
• Dunkl shift operators and Bannai-Ito polynomials (2011, methodology): “1) (acting on the variable z) is the Askey-Wilson difference operator [2], [17].”
• Higher order recurrence relation for exceptional Charlier, Meixner, Hermite and Laguerre orthogonal polynomials (2014, background): “175-7, from where the next formulas can be easily derived; see also [23], pp, 234-7 or [27], ch.”
• Formulae for Askey-Wilson moments and enumeration of staircase tableaux (2010, background): “For other values of a, b, c and d, see [22], page 415.”