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Horowitz reduction is used in indefinite integration to reduce a rational function into polynomial and logarithmic parts. The polynomial part is then trivially integrated, ...

Householder (1953) first considered the matrix that now bears his name in the first couple of pages of his book. A Householder matrix for a real vector v can be implemented ...

A hyperbolic fixed point of a differential equation is a fixed point for which the stability matrix has eigenvalues lambda_1<0<lambda_2, also called a saddle point. A ...

By analogy with the lemniscate functions, hyperbolic lemniscate functions can also be defined arcsinhlemnx = int_0^x(1+t^4)^(1/2)dt (1) = x_2F_1(-1/2,1/4;5/4;-x^4) (2) ...

The expected value B_n(s) of r^s from a fixed vertex of a unit n-cube to a point picked at random in the interior of the hypercube is given by B_n(s) = ...

z(1-z)(d^2y)/(dz^2)+[c-(a+b+1)z](dy)/(dz)-aby=0. It has regular singular points at 0, 1, and infty. Every second-order ordinary differential equation with at most three ...

A relation expressing a sum potentially involving binomial coefficients, factorials, rational functions, and power functions in terms of a simple result. Thanks to results by ...

A hypergeometric series sum_(k)c_k is a series for which c_0=1 and the ratio of consecutive terms is a rational function of the summation index k, i.e., one for which ...

The identity function id(x) is the function id(x)=x which assigns every real number x to the same real number x. It is identical to the identity map. The identity function is ...

Implicit differentiation is the procedure of differentiating an implicit equation with respect to the desired variable x while treating the other variables as unspecified ...