The Associated Ultraspherical Polynomials and their q-Analogues
1982 ◽
Vol 34
(3)
◽
pp. 718-736
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Keyword(s):
A sequence of polynomials {Pn(x)} is orthogonal if Pn(x) is of precise degree n and there is a finite positive measure dμ such that1.1A necessary and sufficient condition for orthogonality [9] is that {Pn(x)} satisfies a three term recurrence1.2with1.3Given a sequence of orthogonal polynomials {Pn(x)} satisfying (1.2), the associated polynomials {Pn(γ)(x)}, γ > 0, are defined by1.4with P(γ)-1(x) = 0, P0(γ)(x) = 1, when An+γ and Bn+γ are well-defined.
1990 ◽
Vol 32
(2)
◽
pp. 180-192
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1980 ◽
Vol 88
(1)
◽
pp. 33-43
◽
1990 ◽
Vol 42
(2)
◽
pp. 315-341
◽
1979 ◽
Vol 31
(2)
◽
pp. 255-263
◽
1978 ◽
Vol 26
(1)
◽
pp. 31-45
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1972 ◽
Vol 18
(2)
◽
pp. 129-136
◽
1981 ◽
Vol 89
(1-2)
◽
pp. 25-50
◽
1996 ◽
Vol 39
(3)
◽
pp. 275-283
◽
1963 ◽
Vol 6
(2)
◽
pp. 267-273
◽
2013 ◽
Vol 2013
◽
pp. 1-6
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