Start with Glasser’s hypergeometric solution to the general quintic:

(assume that you’ve already performed the Tschirnhausen transformation)

(the signs are wrong on the wikipedia page. they have been corrected below)

I was reading Gasper’s *Basic Hypergeometric Series*, and since I’ve been playing around (amongst other things) with the hypergeometric solution to the quintic, and in the first few pages Gasper mentions -hypergeometric functions, the question leapt into my mind: *What would happen if we take the -analogue of the Glasser’s method hypergeometric solution, in other words:*

The idea here would be to choose a fixed , one whose roots were all within the unit disk, and then to make five phase portraits of their -analogues

Remark: I am tempted to look at cases where because all of those fractional powers will vanish

Additionally, suppose we were to get into Bring form and then solve that with the non--analogized version.(matrix identity to be worked out soon)