Conociendo mejor a los q

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Chapter 2
The Classical Basic Hypergeometric
Orthogonal Polynomials
qR
AW
cqHa
cdqHa
ASC
qMP
cbqHe
cqL
cqHe
cqJ
F
qHa
bqJ
bqL
lqJ
qM
qK
lqL
qL
qB
qC
SW
F
dqHa
F
QqK
F
AqK
F
dqK
ASCI
ASCII
dqHeI
dqHeII
F
F
Info: relevant, squared: q−linear lattice, almost squared: quadratic lattice, oval:
q −1 −linear lattice. Red line: particular case, black line: limiting case, orange line: if the
first is on q, the second is on q −1 , blue lines: we discovered (new!), F: blunt orthogonality.
Conociendo mejor a los q-polinomios
Roberto S. Costas Santos
Abbreviations:
AW≡ Askeyi–Wilson, qR≡ q−Racah,
cdqHa≡continuous dual q−Hahn, cqHa≡continuous q−Hahn, biqJ≡big q−Jacobi,
qHa≡ q−Hahn, dqHa≡dual q−Hahn,
ASC≡Al–Salam Chihara, qMP≡q−Meixner–Pollaczek, cqJ≡continuous q−Jacobi,
bqL≡ big q−Laguerre, lqJ≡little q−Jacobi, qM≡ q−Meixner, qK≡ q−Krawtchouk
QqK≡quantum q−Krawtchouk, AqK≡Affine q−Krawtchiuk, dqK≡dual q−Krawtchouk,
cbqHe≡continuous big q−Hermite, cqL≡continuous q−Laguerre, lqL≡little q−Laguerre,
qL≡ q−Laguerre,
qB≡ q−Bessel,
qC≡ q−Charlier, ASCI≡Al–Salam-Carlitz I,
ASCII≡Al–Salam-Carlitz II, cqHe≡continuous q−Hermite, SW≡Stieltjes–Wigert,
dqHeI≡discrete q−Hermite I, dqHeII≡discrete q−Hermite II.
Universidad de Alcalá
V encuentro iberoamericano de polinomios ortogonales
y sus aplicaciones 8 de Junio, 2015, Mexico
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