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Formulas obtained from differentiating Newton's forward difference formula, where R_n^'=h^nf^((n+1))(xi)d/(dp)(p; n+1)+h^(n+1)(p; n+1)d/(dx)f^((n+1))(xi), (n; k) is a ...

Kummer's first formula is (1) where _2F_1(a,b;c;z) is the hypergeometric function with m!=-1/2, -1, -3/2, ..., and Gamma(z) is the gamma function. The identity can be written ...

There exist a variety of formulas for either producing the nth prime as a function of n or taking on only prime values. However, all such formulas require either extremely ...

There are many formulas of pi of many types. Among others, these include series, products, geometric constructions, limits, special values, and pi iterations. pi is ...

Combinatorial topology is a subset of algebraic topology that uses combinatorial methods. For example, simplicial homology is a combinatorial construction in algebraic ...

For n a positive integer, expressions of the form sin(nx), cos(nx), and tan(nx) can be expressed in terms of sinx and cosx only using the Euler formula and binomial theorem. ...

Combinatorial geometry is a blending of principles from the areas of combinatorics and geometry. It deals with combinations and arrangements of geometric objects and with ...

Binet's first formula for the log gamma function lnGamma(z), where Gamma(z) is a gamma function, is given by for R[z]>0 (Erdélyi et al. 1981, p. 21; Whittaker and Watson ...

Combinatorial game theory is the theory of two-player games of perfect knowledge such as go, chess, or checkers.

Combinatorial matrix theory is a rich branch of mathematics that combines combinatorics, graph theory, and linear algebra. It includes the theory of matrices with prescribed ...