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semiconvergent

noun

Etymology

From semi- + convergent.

Definitions

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

    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.

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

The neighborhood

Vish — recursive loop

No curated loop yet for semiconvergent. Loops are being traced one word at a time while the ingestion pipeline matures.

sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA