closed form function | hypergeometric

A discrete function A(n, k) is called closed form (or sometimes "hypergeometric") in two variables if the ratios A(n + 1, k)/A(n, k) and A(n, k + 1)/A(n, k) are both rational functions. A pair of closed form functions (F, G) is said to be a Wilf-Zeilberger pair if F(n + 1, k) - F(n, k) = G(n, k + 1) - G(n, k). The term "hypergeometric function" is less commonly used to mean "closed form, " and "hypergeometric series" is sometimes used to mean hypergeometric function. A differential k-form α is said to be a closed form if d α = 0.

closed-form solution | differential k-form | elementary number | hypergeometric differential equation | hypergeometric distribution | hypergeometric function | hypergeometric summation | hypergeometric term | Liouvillian number | rational function | Wilf-Zeilberger pair