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QDifferenceEquations[AccurateQSummation] - sum the solutions of a q-shift operator
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Calling Sequence
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AccurateQSummation(L, Q, x)
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Parameters
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L
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polynomial in Q over C(q)(x)
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Q
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name; denote the q-shift operator
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x
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name (that Q acts on)
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Description
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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.
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Q is the q-shift operator with respect to x, defined by  .
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Examples
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![Ac := [q^4/(q^4-q^3-q+1)-(q^2+1)*q*Q/(q^4-q^3-q+1)+Q^2/(q^4-q^3-q+1), (q^3+q-1)/(q^4-q^3-q+1)-Q/(q^4-q^3-q+1)]](/support/helpjp/helpview.aspx?si=8736/file02637/math128.png)
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Regarding the meaning of the second element rt in the output of AccurateQSummation, since  is the minimal annihilator of  ,  is an anti-qdifference of  :
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![A := OreTools:-SetOreRing([x, q], 'qshift')](/support/helpjp/helpview.aspx?si=8736/file02637/math157.png)
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check that  :
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References
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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.
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