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The number of nonassociative n-products with k elements preceding the rightmost left parameter is F(n,k) = F(n-1,k)+F(n-1,k-1) (1) = (n+k-2; k)-(n+k-1; k-1), (2) where (n; k) ...

Let P be a polynomial of degree n with derivative P^'. Then ||P^'||_infty<=n||P||_infty, where ||P||_infty=max_(|z|=1)|P(z)|.

The parameter r (sometimes also denoted mu) in the logistic equation x_(n+1)=rx_n(1-x_n).

(1) Based on or involving trial and error. (2) Convincing without being rigorous.

A polynomial x^n+a_(n-1)x^(n-1)+...+a_1x+a_0 in which the coefficient of the highest order term is 1.

In order to find a root of a polynomial equation a_0x^n+a_1x^(n-1)+...+a_n=0, (1) consider the difference equation a_0y(t+n)+a_1y(t+n-1)+...+a_ny(t)=0, (2) which is known to ...

An encoding is a way of representing a number or expression in terms of another (usually simpler) one. However, multiple expressions can also be encoded as a single ...

The "Foxtrot series" is a mathematical sum that appeared in the June 2, 1996 comic strip FoxTrot by Bill Amend (Amend 1998, p. 19; Mitchell 2006/2007). It arose from a ...

A matrix H with elements H_(ij)=(i+j-1)^(-1) (1) for i,j=1, 2, ..., n. Hilbert matrices are implemented in the Wolfram Language by HilbertMatrix[m, n]. The figure above shows ...

A Lucas polynomial sequence is a pair of generalized polynomials which generalize the Lucas sequence to polynomials is given by W_n^k(x) = ...