This AccurateQSummation(L,Q,x) calling sequence computes an operator M of minimal order such that any solution  of L has an anti-qdifference which is a solution of M.

If the order of L equals the order of M then the output is a list [M, r] such that r(f) is an anti-qdifference of  and also a solution of M for every solution  of L. If the order of L is not equal to M then only M is given in the output. In this case M equals  where .

Q is the q-shift operator with respect to x, defined by .

Abramov, S.A., and van Hoeij, M. "Integration of Solutions of Linear Functional Equations." Integral Transformations and Special Functions. Vol. 8 No. 1-2. (1999): 3-12.