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There are several meanings of "null vector" in mathematics. 1. The most common meaning of null vector is the n-dimensional vector 0 of length 0. i.e., the vector with n ...

Following the work of Fuchs in classifying first-order ordinary differential equations, Painlevé studied second-order ordinary differential equation of the form ...

The parabolic cylinder differential equation is the second-order ordinary differential equation y^('')+(nu+1/2-1/4z^2)y=0 (1) whose solution is given by ...

An auxiliary latitude also called the reduced latitude and denoted eta or theta. It gives the latitude on a sphere of radius a for which the parallel has the same radius as ...

The golden ratio phi can be written in terms of a nested radical in the beautiful form phi=sqrt(1+sqrt(1+sqrt(1+sqrt(1+...)))), (1) which can be written recursively as ...

A skewed distribution which is similar to the binomial distribution when p!=q (Abramowitz and Stegun 1972, p. 930). y=k(t+A)^(A^2-1)e^(-At), (1) for t in [0,infty) where A = ...

Polynomials s_k(x;lambda,mu) which are a generalization of the Boole polynomials, form the Sheffer sequence for g(t) = (1+e^(lambdat))^mu (1) f(t) = e^t-1 (2) and have ...

Polynomials P_k(x) which form the Sheffer sequence for g(t) = (2t)/(e^t-1) (1) f(t) = (e^t-1)/(e^t+1) (2) and have generating function ...

A prime factorization algorithm which can be implemented in a single-step or double-step form. In the single-step version, a prime factor p of a number n can be found if p-1 ...

The (signed) area of a planar non-self-intersecting polygon with vertices (x_1,y_1), ..., (x_n,y_n) is A=1/2(|x_1 x_2; y_1 y_2|+|x_2 x_3; y_2 y_3|+...+|x_n x_1; y_n y_1|), ...