X-Nico

Dobinski's formula

The number on both sides of the formula has come to be called the nth Bell number B_n, after the later work of Eric Temple Bell.

Giambelli's formula

In mathematics, Giambelli's formula, named after Giovanni Giambelli, expresses Schubert classes in terms of special Schubert classes, or Schur functions in terms of complete symmetric functions.

Jensen's formula

which is the Poisson formula for the harmonic function $f(z)|$.

Kirchhoff's theorem

Cayley's formula follows from Kirchhoff's theorem as a special case, since every vector with 1 in one place, −1 in another place, and 0 elsewhere is an eigenvector of the Laplacian matrix of the complete graph, with the corresponding eigenvalue being n.

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It is a generalization of Cayley's formula which provides the number of spanning trees in a complete graph.

Pseudoforest

André Joyal used this fact to provide a bijective proof of Cayley's formula, that the number of undirected trees on n nodes is n^n − 2, by finding a bijection between maximal directed pseudoforests and undirected trees with two distinguished nodes.

Savitzky–Golay filter

The summations in the matrix J^TJ can be evaluated in closed form,

Serial offender hunting patterns

Criminologist D. Kim Rossmo created the “Rossmo Formula” to explain his ideas on serial offenders and geographic profiling to determine where criminals lived and why specific locations were chosen as places to commit crimes.

Sums of powers

Faulhaber's formula expresses $1^k\; +\; 2^k\; +\; 3^k\; +\; \backslash cdots\; +\; n^k$ as a polynomial in n.

see also