Standard Lemma guide

semiconvergent

adj · noun · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

adj

Meaning 1

For which the limit lim _(k→∞) bold Tk exists.

Definition source: English Wiktionary via Wiktextract

Usage: not-comparable

Topics: mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

A kind of fraction. If (h_n-1)/(k_n-1), (h_n)/(k_n) are successive convergents, then any fraction of the form (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.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, sciences

Examples

  • The semiconvergents to the continued fraction expansion of a real number include all the rational approximations which are better than any approximation with a smaller denominator.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

From semi- + convergent.