Determination of [nθ] by its Sequence of*Differences

Canadian Mathematical Bulletin - Tập 21 Số 4 - Trang 441-446 - 1978
Aviezri S. Fraenkel1, M. Mushkin1, Uzi Tassa1
1Department of Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel

Tóm tắt

AbstractFor any real numberθletwhere [x] denotes the greatest integer not exceedingx.A method is given for computingfθfrom its first few terms. A similar method is given for computing the characteristic functiongθ(n)of[nθ]. The given methods converge rapidly, and generalize previous results of Bernoulli, Markorf, and Stolarsky. Note that either of the sequencesfθand gθdetermines the sequence[nθ] (n = 1, 2,…).

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