Search Results for ""

The hexanacci numbers are a generalization of the Fibonacci numbers defined by H_0=0, H_1=1, H_2=1, H_3=2, H_4=4, H_5=8, and the recurrence relation ...

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 root-finding algorithm based on the iteration formula x_(n+1)=x_n-(f(x_n))/(f^'(x_n)){1+(f(x_n)f^('')(x_n))/(2[f^'(x_n)]^2)}. This method, like Newton's method, has poor ...

Let |A| denote the cardinal number of set A, then it follows immediately that |A union B|=|A|+|B|-|A intersection B|, (1) where union denotes union, and intersection denotes ...

The identity _2F_1(x,-x;x+n+1;-1)=(Gamma(x+n+1)Gamma(1/2n+1))/(Gamma(x+1/2n+1)Gamma(n+1)), or equivalently ...

A root-finding algorithm which converges to a complex root from any starting position. To motivate the formula, consider an nth order polynomial and its derivatives, P_n(x) = ...

A (general, asymmetric) lens is a lamina formed by the intersection of two offset disks of unequal radii such that the intersection is not empty, one disk does not completely ...

Given a point P and a line AB, draw the perpendicular through P and call it PC. Let PD be any other line from P which meets CB in D. In a hyperbolic geometry, as D moves off ...

Macdonald's plane partition conjecture proposes a formula for the number of cyclically symmetric plane partitions (CSPPs) of a given integer whose Ferrers diagrams fit inside ...

There are several different kinds of magic numbers. The digital root and magic constant are sometimes known as magic numbers. In baseball, the magic number for a team in ...