semiconvergent

Meanings

Noun

• A kind of fraction. If $\backslash frac\{h\_\{n-1\}\; \}\{k\_\{n-1\}\; \}$, $\backslash frac\{h\_n\}\{k\_n\}$ are successive convergents, then any fraction of the form $\backslash frac\{h\_\{n-1\}\; +\; ah\_n\}\{k\_\{n-1\}\; +\; ak\_n\}$, where a is a nonnegative integer and the numerators and denominators are between the n and n+1 terms inclusive, is a semiconvergent.

Adjective

• For which the limit $\backslash lim\_\{k\; \backslash to\; \backslash infty\}\; \backslash bold\; T^k$ exists.

Origin

• semi- + convergent