The 
-Whipple
transformation is the identity
![_8phi_7[a,qa^(1/2),-qa^(1/2),b,c,d,e,q^(-N); a^(1/2),-a^(1/2),(aq)/b,(aq)/c,(aq)/d,(aq)/e,aq^(N+1);q,(aq^(N+2))/(bcde)]
=(((aq)/(de);q)_N)/(((aq)/d;q)_N((aq)/e;q)_N)_4phi_3[d,e,(aq)/(bc),q^(-N); (aq)/b,(aq)/c,deq^(-n)/a;q,q],](/images/equations/q-WhippleTransformation/NumberedEquation1.svg) |
where 
is a q-hypergeometric function.
q-Whipple Transformation
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References
Bhatnagar, G. "Inverse Relations, Generalized Bibasic Series, and Their
Extensions." PhD thesis. Columbus, OH: Ohio State
University, p. 35, 1995.Gasper, G. and Rahman, M. Basic
Hypergeometric Series. Cambridge, England: Cambridge University Press, p. 35,
1990.Referenced on Wolfram|Alpha
q-Whipple TransformationCite this as:
Weisstein, Eric W. "q-Whipple Transformation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/q-WhippleTransformation.html