Word Pronunciation & Dictionary

semiconvergent

Word Rarity Very rare

Frequency: Zipf frequency 0.00 in modern English

Syllables: semi-con-ver-gent
IPA

22

Scrabble Score

14

Letters

4

Syllables

11

Unique Chars

Meaning

noun

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.

adj

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

Example Sentences

"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."

Etymology

From semi- + convergent.

Word Breakdown

Prefix: semi

Inflected Forms

semiconvergents (plural)

Questions

What does semiconvergent mean?: 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.
Where does semiconvergent come from?: From semi- + convergent.

How to pronounce semiconvergent

Open the pronunciation page — Open the Speakur entry for “semiconvergent”.
Read the phonetic spelling — Read the IPA spelling () so you know which sounds to aim for.
Play the audio — Click Play to hear reference audio for “semiconvergent”.
Repeat and practice — Say “semiconvergent” aloud, matching stress and vowels until it feels natural.