Semiconvergent

English

Etymology

From Template:Prefix.

Noun

1. Template:Lb A kind of fraction. If $\frac{h_{n-1}}{k_{n-1}}$, $\frac{h_n}{k_n}$ are successive convergents, then any fraction of the form $\frac{h_{n-1}+a{h}_n}{k_{n-1}+a{k}_n}$, where a is a nonnegative integer and the numerators and denominators are between the n and n+1 terms inclusive, is a semiconvergent.

   Template:Ux

Adjective

1. Template:Lb For which the limit $\underset{k\to \mathrm{\infty }}{\lim }{𝐓}^k$ exists.