Examine zeros, gamma expansions, recurrences, and OEIS connections — exact computations run locally in your browser.
PolynomialEnter coefficients in ascending degree, or an expanded polynomial.
iTries increasingly complex recurrence shapes, starting from the simplest. Polynomial sequences use bounds up to depth 10, t-degree 5, n-degree 5, and derivative order 5; integer sequences use scalar recurrences in n. There is no time or candidate-count cutoff: it stops at the first match or after exhausting the bounded search. An unsuccessful exhaustive search can take a long time; use Cancel to stop it.iSet exact search bounds yourself. Useful when you know the expected recurrence shape or want to explore a specific search space.
iMaximum number of previous terms P(n−1), P(n−2), … the recurrence may reference.iMaximum degree in the polynomial variable t for each coefficient a_k(n, t).iMaximum degree in the index n for each coefficient a_k(n, t).iMaximum order of the derivative operator D = d/dt applied to terms. Allows recurrences involving P(n−k), P′(n−k), P″(n−k), …
iAllow a common denominator on the left-hand side: f(n, t) P(n) = ∑ a_k(n, t) P(n−k). Finds recurrences with rational function coefficients in n and t.iAllow an additive term g(n, t) on the right-hand side: ∑ a_k(n,t) P(n−k) = g(n, t). Slower search but finds more recurrences.iAlso allow right-hand-side terms multiplied by (-1)n, such as (-1)n a_k(n, t) P(n−k). Useful for alternating or parity-sensitive sequences.