Continued fraction expansions for the complete, incomplete, and relativistic plasma dispersion functions

1984 ◽  
Vol 25 (3) ◽  
pp. 466-468 ◽  
Author(s):  
Anthony L. Peratt
Keyword(s):  
Continued Fraction ◽  
Relativistic Plasma ◽  
Continued Fraction Expansions ◽  
Plasma Dispersion

Continued fraction expansions for the plasma dispersion function

1984 ◽  
Vol 32 (3) ◽  
pp. 479-485 ◽  
Author(s):  
J. H. McCabe
Keyword(s):  
Error Estimates ◽  
Continued Fraction ◽  
Dispersion Function ◽  
Simple Expansion ◽  
Continued Fraction Expansions ◽  
Plasma Dispersion

Two continued fraction expansions for the plasma dispersion function are given. The first is a very simple expansion for which error estimates can be obtained and which provides better approximations as the modulus of the argument increases. The second, while not so simple, provides whole range approximations.

scholarly journals A Lochs-Type Approach via Entropy in Comparing the Efficiency of Different Continued Fraction Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 255
Author(s):  
Dan Lascu ◽  
Gabriela Ileana Sebe
Keyword(s):  
Dynamical Systems ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Unit Interval ◽  
Probability Measures ◽  
Absolutely Continuous ◽  
Continued Fraction Expansions ◽  
Absolutely Continuous Invariant

We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964. Thus, we aim to compare the efficiency by describing the rate at which the digits of one number-theoretic expansion determine those of another. We study Chan’s continued fractions, θ-expansions, N-continued fractions, and Rényi-type continued fractions. A central role in fulfilling our goal is played by the entropy of the absolutely continuous invariant probability measures of the associated dynamical systems.

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