Continuant

A continuant is a speech sound produced with an incomplete closure of the oral vocal tract. Among consonants, there are two broad categories of continuants: fricatives and approximants. Approximants are sometimes called "frictionless continuants".

Compare sonorant (resonant), which includes approximants and nasals but not fricatives. Both terms technically include vowels, but are frequently restricted to the context of consonants.

See also

Source

Continuant (mathematics)

In algebra, the continuant is a multivariate polynomial representing the determinant of a tridiagonal matrix and having applications in generalized continued fractions.

Definition

The n-th continuant is defined recursively by

Properties

Continuant can be computed by taking the sum of all possible products of x₁,...,x_n, in which any number of disjoint pairs of consecutive terms are deleted (Euler's rule). For example,

, the (n+1)-st Fibonacci number.

Generalizations

An generalized definition takes the continuant with respect to three sequences a, b and c, so that K(n) is a polynomial of a₁,...,a_n, b₁,...,b_n−1 and c₁,...,c_n−1. In this case the recurrence relation becomes

Since b_r and c_r enter into K only as a product b_rc_r there is no loss of generality in assuming that the b_r are all equal to 1.