recurrence relation

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recurrence relation

[ri′kər·əns ri‚lā·shən]
(mathematics)
An equation relating a term in a sequence to one or more of its predecessors in the sequence.
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For example, when a is a finitely supported sequence, Equation (6) is a recurrence equation in b, that has many solutions even if [?
Example applications of an algorithm to determine whether a three-term recurrence equation has solutions in the Hahn class-implemented in the computer algebra system Maple-are given.
From the differential or (q)-difference equation one can determine the three-term recurrence equation for [P.
Keywords Generalized constructive set, summation, recurrence equation, characteristic equation.
Combining (1) and (2), we can get the following recurrence equation
Appendix B: The Coefficients of the Recurrence Equation.
Appendix C: The Coefficients of the Recurrence Equations.
Comparing this recurrence relation with the recurrence equation
In Section 2, we present a simple recurrence equation for [F.
As a final general remark, let us point out that a power series satisfies a linear differential equation if and only if its coefficients satisfy a linear recurrence equation with polynomial coefficients.
Isotropic initial conditions allow simplification of the formal derivative of the four hexahdron recurrence equations with respect to a parameter t.
For such loops, (i) the polynomial invariant ideal over the scalar variables is derived by omitting loop tests and deploying recurrence solving algorithms, and (ii) quantified loop invariants over arrays are inferred by using loop tests in conjunction with the recurrence equations of scalars.