Classical and Quantum Orthogonal Polynomials in One Variable: Bibliography

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Askey--Wilson polynomials, quadratic harnesses and martingales (2008, methodology): “ake b=0 and all other parameters nonzero to write c¯k,n =(−1)kqk(k+1)/2 (aec,a de)n(q−n)k an−k 3 ϕ 2 qk−n,acqk,adqk aecqk,adqek ;q (A.11) . Then we apply the limiting case of Sears transformation [17], Theorem 12.4.2, to rewrite 3ϕ 2 qk− n,acqk,adqk aecq k,adqe ;q = (adqk) −k(d/de ) n−k (adqek) ”
Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux–Crum transformations (2010, unknown): “[24]).”
The Analytic Theory of Matrix Orthogonal Polynomials (2007, background): “X ORTHOGONAL POLYNOMIALS 3 There is very littleonthesubject inmonographs —the moreclassical ones (e.g., [23, 82, 93, 184]) predate most of the subject; see, however, Atkinson [5, Section 6.6]. Ismail [118] has no discussion and Simon [167, 168] has a single section! Because of the use of MOPRL in [3”
THE FERMAT CUBIC, ELLIPTIC FUNCTIONS, CONTINUED FRACTIONS, AND A COMBINATORIAL EXCURSION (2005, unknown): “ccurrence in (45) of the fundamental Abelian integral from which sm,cm are deﬁned is especially striking. As shown in [28, 29], the moment problem is indeterminate; see also Ismail’s forthcoming book [32] for a perspective. Conclusion. We have studied a class of continued fraction with sextic numera”