sumtools[hyperrecursion] - Zeilberger-Koepf's hyperrecursion algorithm
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Calling Sequence
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hyperrecursion(U, L, z, s(n))
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Parameters
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U, L
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lists of the upper and lower parameters
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z
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evaluation point
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n
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name, recurrence variable
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s
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name, recurrence function
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Description
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This function is an implementation of Koepf's extension of Zeilberger's algorithm, calculating a (downward) recurrence equation for the sum
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the sum to be taken over all integers k, with respect to n. Here, U and L denote the lists of upper and lower parameters, and z is the evaluation point. The arguments of U and L are assumed to be rational-linear with respect to n. The resulting expression equals zero.
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The output is a recurrence which equals zero. The recurrence is output as a function of n, the recurrence variable, and .
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The command with(sumtools,hyperrecursion) allows the use of the abbreviated form of this command.
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Examples
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| (1) |
Dougall's identity
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![hyperrecursion([a, 1+(1/2)*a, b, c, d, 1+2*a-b-c-d+n, -n], [(1/2)*a, 1+a-b, 1+a-c, 1+a-d, 1+a-1-2*a+b+c+d-n, 1+a+n], 1, s(n))](/support/helpjp/helpview.aspx?si=6529/file04495/math119.png)
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| (2) |
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![hyperrecursion([a+1/2, a, b, 1-b, -n, (1+2*a)*(1/3)+n, 1+(1/2)*a], [1/2, (2*a-b+3)*(1/3), (2*a+b+2)*(1/3), -3*n, 2*a+1+3*n, (1/2)*a], 1, s(n))](/support/helpjp/helpview.aspx?si=6529/file04495/math126.png)
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| (3) |
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