Convergence rate for Rényi-type continued fraction expansions
نویسندگان
چکیده
منابع مشابه
Large Deviation Asymptotics for Continued Fraction Expansions
We study large deviation asymptotics for processes defined in terms of continued fraction digits. We use the continued fraction digit sum process to define a stopping time and derive a joint large deviation asymptotic for the upper and lower fluctuation process. Also a large deviation asymptotic for single digits is given.
متن کاملContinued Fraction Expansions of Matrix Eigenvectors
We examine various properties of the continued fraction expansions of matrix eigenvector slopes of matrices from the SL(2, Z) group. We calculate the average period length, maximum period length, average period sum, maximum period sum and the distributions of 1s 2s and 3s in the periods versus the radius of the Ball within which the matrices are located. We also prove that the periods of contin...
متن کاملOn the real quadratic fields with certain continued fraction expansions and fundamental units
The purpose of this paper is to investigate the real quadratic number fields $Q(sqrt{d})$ which contain the specific form of the continued fractions expansions of integral basis element where $dequiv 2,3( mod 4)$ is a square free positive integer. Besides, the present paper deals with determining the fundamental unit$$epsilon _{d}=left(t_d+u_dsqrt{d}right) 2left.right > 1$$and $n_d$ and $m_d...
متن کاملContinued fraction expansions for q-tangent and q-cotangent functions
1 Philippe Flajolet and continued fractions In a paper that was written on the occasion of Philippe Flajolet’s 50th birthday [26] and discussed his various research areas, we wrote about his contributions to continued fractions: Continued fractions The papers [8, 9, 10] deal with the interplay of continued fractions and combinatorics. Let us consider lattice paths, consisting of steps NORTHEAST...
متن کاملContinued-fraction Expansions for the Riemann Zeta Function and Polylogarithms
It appears that the only known representations for the Riemann zeta function ζ(z) in terms of continued fractions are those for z = 2 and 3. Here we give a rapidly converging continued-fraction expansion of ζ(n) for any integer n ≥ 2. This is a special case of a more general expansion which we have derived for the polylogarithms of order n, n ≥ 1, by using the classical Stieltjes technique. Our...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Periodica Mathematica Hungarica
سال: 2020
ISSN: 0031-5303,1588-2829
DOI: 10.1007/s10998-020-00325-2