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Askey-Wilson functions of the first and second kind: Series and integral representations of \(C^ 2_ n(x ;\beta{}|{}q)+D^ 2_ n(x ;\beta{}|{}q)\). (English) Zbl 0765.33012

The author finds series and integral representations for the Askey-Wilson functions of first and second kind, namely, \(C_ n^ 2(x;\beta\mid q)\) and \(D_ n^ 2(x;\beta\mid q)\). The functions are expressed in terms of a particular \(_ 5\Phi_ 4\). The integral representation makes use of a well known representation due to Askey. The expression (4.1) for the square of \(| S_ \lambda|\) seems to have some printing errors. It is also not mentioned that the parameter ‘\(a\)’ in (4.1) is a real and not a complex number.

MSC:

33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
33C55 Spherical harmonics
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