A note on some results involving basic hypergeometric functions (Q1262984)

The decomposition of hypergeometric series into odd and even parts has been the object of study of various authors with a view of obtaining reduction formulae for hypergeometric functions of higher order. See, for example, \textit{T. J. Lardner}, SIAM Rev. 11, 69-72 (1969; Zbl 0176.017). In this study this technique is applied to q-hypergeometric series of quite general type. Interesting special cases are discussed, in particular a relation between q-analogues of Bessel functions and q- Kelvin functions. A generalization of the main result is given.