Overview
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FSums
A Mathematica package for determining inhomogeneous recurrences for nested sums over hypergeometric terms with nonstandard boundary conditions by Flavia Stan
Usage instructions

UseMultiSum[fIn, N, listSumVars]
computes a recurrence by calling theFindRecurrence
andFindStructureSet
functions from the packageMultiSum
. The list of summation variables can be reordered later by theArrange
functions. 
ShiftToPositive[rec, N, varList]
uses theShiftRecurrence
command fromMultiSum
to shift the recurrencerec
such that it contains only positive shifts. 
Arrange[rec, range]
arranges the notation for the F's appearing inrec
such that we haveF[N, listSumVars]
wherelistSumVars
is given by range. This is used if the certificate recurrence was computed using an order of variables different from the one given by the range. 
InhRecurrence[rec, N, range, CoeffBound > const]
delivers a inhomogeneous recurrence starting with the certificate recurrencerec
in the variableN
. Ifconst>0
the functionSplitLargeCoeff
is applied for large polynomial coefficients inside the delta parts.CoeffBound
: Option for theInhRecurrence
function. Default value is 0 to obtain the smallest number of FSums in the inhomogeneous part of the recurrence. 
FSum[summand, range]
structure for the nested sums where the range is given as a list of the form{{sig, 0, Infinity}, {j,0,N2}, {k,0,j+1},{l,0,Nk}}
. 
SubstituteSummandInRec[rec, fIn, N, listSumVars]
substitutes the summandfIn
asF[N, listSumVars]
in the recurrencerec
.
Software requirements
The package works best in combination with the RISC Algorithmic Combinatorics Software Package MultiSum