## 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