• Source: Big q-Jacobi polynomials

In mathematics, the big q-Jacobi polynomials Pn(x;a,b,c;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme.




Definition


The polynomials are given in terms of basic hypergeometric functions by






P

n


(
x
;
a
,
b
,
c
;
q
)
=





3



ϕ

2


(

q

−
n


,
a
b

q

n
+
1


,
x
;
a
q
,
c
q
;
q
,
q
)



{\displaystyle \displaystyle P_{n}(x;a,b,c;q)={}_{3}\phi _{2}(q^{-n},abq^{n+1},x;aq,cq;q,q)}





References






Further reading


Gasper, George; Rahman, Mizan (2004), Basic hypergeometric series, Encyclopedia of Mathematics and its Applications, vol. 96 (2nd ed.), Cambridge University Press, ISBN 978-0-521-83357-8, MR 2128719
Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F. (2010), "9.8 Jacobi", Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics, Berlin, New York: Springer-Verlag, pp. 216–221, doi:10.1007/978-3-642-05014-5, ISBN 978-3-642-05013-8, MR 2656096 gives a detailed list of properties.
Koornwinder, Tom H.; Wong, Roderick S. C.; Koekoek, Roelof; Swarttouw, René F. (2010), "Chapter 18: Orthogonal Polynomials", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0-521-19225-5, MR 2723248.

Kata Kunci Pencarian:

• Big q-Jacobi polynomials
• Jacobi polynomials
• Q-Jacobi polynomials
• List of q-analogs
• List of things named after Carl Gustav Jacob Jacobi
• Orthogonal polynomials
• Legendre polynomials
• Chebyshev polynomials
• Askey scheme
• Faulhaber's formula