If at least one of 
, 
, or 
has the form 
for some nonnegative integer 
(in which case both sums terminate after 
terms), then
![_8phi_7[a,qa^(1/2),-qa^(1/2),b,c,d,e,f; a^(1/2),-a^(1/2),(aq)/b,(aq)/c,(aq)/d,(aq)/e,(aq)/f;q,(a^2q^2)/(bcdef)]
=((aq,(aq)/(de),(aq)/(df),(aq)/(ef))_infty)/(((aq)/d,(aq)/e,(aq)/f,(aq)/(def))_infty)_4phi_3[(aq)/(bc),d,e,f; (aq)/b,(aq)/c,(def)/a;q,q],](/images/equations/Watson-WhippleTransformation/NumberedEquation1.svg) |
where 
is a generalized q-Pochhammer symbol
 |
and each of 
and 
is a q-hypergeometric
function.
Watson-Whipple Transformation
See also
q-Hypergeometric Function, q-Pochhammer Symbol, q-SeriesExplore with Wolfram|Alpha
References
Gasper, G. and Rahman, M. Basic Hypergeometric Series. Cambridge, England: Cambridge University Press, p. 242, 1990.Gordon, B. and McIntosh, R. J. "Some Eighth Order Mock Theta Functions." J. London Math. Soc. 62, 321-335, 2000.Referenced on Wolfram|Alpha
Watson-Whipple TransformationCite this as:
Weisstein, Eric W. "Watson-Whipple Transformation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Watson-WhippleTransformation.html