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(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) = ...

Dissect a triangle into smaller triangles, such that all have full edge contact with their neighbors. Label the corners 1, 2, and 3. Label all vertices with 1, 2, or 3, with ...

For c<1, x^c<1+c(x-1). For c>1, x^c>1+c(x-1).

The Somos sequences are a set of related symmetrical recurrence relations which, surprisingly, always give integers. The Somos sequence of order k, or Somos-k sequence, is ...