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An equivalence relation on a set X is a subset of X×X, i.e., a collection R of ordered pairs of elements of X, satisfying certain properties. Write "xRy" to mean (x,y) is an ...

A generalization of Turán's theorem to non-complete graphs.

The second-order ordinary differential equation y^('')+2xy^'-2ny=0, (1) whose solutions may be written either y=Aerfc_n(x)+Berfc_n(-x), (2) where erfc_n(x) is the repeated ...

The "imaginary error function" erfi(z) is an entire function defined by erfi(z)=-ierf(iz), (1) where erf(z) is the erf function. It is implemented in the Wolfram Language as ...

Given a Poisson distribution with a rate of change lambda, the distribution function D(x) giving the waiting times until the hth Poisson event is D(x) = ...

Given a formula y=f(x) with an absolute error in x of dx, the absolute error is dy. The relative error is dy/y. If x=f(u,v,...), then ...

An object is unique if there is no other object satisfying its defining properties. An object is said to be essentially unique if uniqueness is only referred to the ...

The Euler-Gergonne-Soddy triangle is the right triangle DeltaZFlEv created by the pairwise intersections of the Euler line L_E, Soddy line L_S, and Gergonne line L_G. (The ...

Define I_n=(-1)^nint_0^infty(lnz)^ne^(-z)dz, (1) then I_n=(-1)^nGamma^((n))(1), (2) where Gamma^((n))(z) is the nth derivative of the gamma function. Particular values ...

An implicit method for solving an ordinary differential equation that uses f(x_n,y_n) in y_(n+1). In the case of a heat equation, for example, this means that a linear system ...