semiconvergent

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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.

“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.”

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Meanings

nounsemiconvergent (plural semiconvergents)

plural semiconvergents

  1. mathematicsA 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.

    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.

adjectivesemiconvergent (not comparable)
  1. not comparablemathematicsFor which the limit lim _(k→∞) bold Tᵏ exists.

Origin

From semi- + convergent.

Full word history & related roots →
Cite this entry
APA

semiconvergent. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/semiconvergent

MLA

“semiconvergent.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/semiconvergent. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “semiconvergent,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/semiconvergent.

Source: semiconvergent on Wiktionary, CC BY-SA 4.0.