On approximation by Lüroth series

Karma Dajani; Cor Kraaikamp

Displaying similar documents to “On approximation by Lüroth series”

Global approximations for the γ-order Lognormal distribution

Thomas L. Toulias (2013)

Discussiones Mathematicae Probability and Statistics

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A generalized form of the usual Lognormal distribution, denoted with $_{γ}$ , is introduced through the γ-order Normal distribution $_{γ}$ , with its p.d.f. defined into (0,+∞). The study of the c.d.f. of $_{γ}$ is focused on a heuristic method that provides global approximations with two anchor points, at zero and at infinity. Also evaluations are provided while certain bounds are obtained.

Automata, algebraicity and distribution of sequences of powers

Jean-Paul Allouche, Jean-Marc Deshouillers, Teturo Kamae, Tadahiro Koyanagi (2001)

Annales de l’institut Fourier

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Let $K$ be a finite field of characteristic $p$ . Let $K ((x))$ be the field of formal Laurent series $f (x)$ in $x$ with coefficients in $K$ . That is, $f (x) = \sum_{n = n_{0}}^{\infty} f_{n} x^{n}$ with $n_{0} \in 𝐙$ and $f_{n} \in K (n = n_{0}, n_{0} + 1, \dots)$ . We discuss the distribution of ${({f^{m}})}_{m = 0, 1, 2, \dots}$ for $f \in K ((x))$ , where ${f} : = \sum_{n = 0}^{\infty} f_{n} x^{n} \in K [[x]]$ denotes the nonnegative part of $f \in K ((x))$ . This is a little different from the real number case where the fractional part that excludes constant term (digit of order 0) is considered. We give an alternative proof of a result by De Mathan obtaining the generic...

On the length of rational continued fractions over $_{q} (X)$

S. Driss (2015)

Discussiones Mathematicae - General Algebra and Applications

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Let $_{q}$ be a finite field and $A (Y) \in_{q} (X, Y)$ . The aim of this paper is to prove that the length of the continued fraction expansion of $A (P); P \in_{q} [X]$ , is bounded.

Uniformly convex spiral functions and uniformly spirallike functions associated with Pascal distribution series

Gangadharan Murugusundaramoorthy, Basem Aref Frasin, Tariq Al-Hawary (2022)

Mathematica Bohemica

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The aim of this paper is to find the necessary and sufficient conditions and inclusion relations for Pascal distribution series to be in the classes ${𝒮𝒫}_{p} (α, β)$ and ${𝒰𝒞𝒱}_{p} (α, β)$ of uniformly spirallike functions. Further, we consider an integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.

The right tail exponent of the Tracy–Widom $β$ distribution

Laure Dumaz, Bálint Virág (2013)

Annales de l'I.H.P. Probabilités et statistiques

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The Tracy–Widom $β$ distribution is the large dimensional limit of the top eigenvalue of $β$ random matrix ensembles. We use the stochastic Airy operator representation to show that as $a \to \infty$ the tail of the Tracy–Widom distribution satisfies $P ({𝑇𝑊}_{β} g t; a) = a^{- (3 / 4) β + o (1)} exp (- \frac{2}{3} β a^{3 / 2}) .$

On the limit distribution of the well-distribution measure of random binary sequences

Christoph Aistleitner (2013)

Journal de Théorie des Nombres de Bordeaux

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We prove the existence of a limit distribution of the normalized well-distribution measure $W (E_{N}) / \sqrt{N}$ (as $N \to \infty$ ) for random binary sequences $E_{N}$ , by this means solving a problem posed by Alon, Kohayakawa, Mauduit, Moreira and Rödl.

On asymmetric distributions of copula related random variables which includes the skew-normal ones

Ayyub Sheikhi, Fereshteh Arad, Radko Mesiar (2022)

Kybernetika

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Assuming that $C_{X, Y}$ is the copula function of $X$ and $Y$ with marginal distribution functions $F_{X} (x)$ and $F_{Y} (y)$ , in this work we study the selection distribution $Z \overset{d}{=} (X | Y \in T)$ . We present some special cases of our proposed distribution, among them, skew-normal distribution as well as normal distribution. Some properties such as moments and moment generating function are investigated. Also, some numerical analysis is presented for illustration.

Automatic continued fractions are transcendental or quadratic

Yann Bugeaud (2013)

Annales scientifiques de l'École Normale Supérieure

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We establish new combinatorial transcendence criteria for continued fraction expansions. Let $α = [0; a_{1}, a_{2}, ...]$ be an algebraic number of degree at least three. One of our criteria implies that the sequence of partial quotients ${(a_{ℓ})}_{ℓ \geq 1}$ of $α$ is not ‘too simple’ (in a suitable sense) and cannot be generated by a finite automaton.

5-dissections and sign patterns of Ramanujan's parameter and its companion

Shane Chern, Dazhao Tang (2021)

Czechoslovak Mathematical Journal

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In 1998, Michael Hirschhorn discovered the 5-dissection formulas of the Rogers-Ramanujan continued fraction $R (q)$ and its reciprocal. We obtain the 5-dissections for functions $R (q) R {(q^{2})}^{2}$ and $R {(q)}^{2} / R (q^{2})$ , which are essentially Ramanujan’s parameter and its companion. Additionally, 5-dissections of the reciprocals of these two functions are derived. These 5-dissection formulas imply that the coefficients in their series expansions have periodic sign patterns with few exceptions.

On the computation of moments of the partial non-central $χ$ -square distribution function

Gil, Amparo, Segura, Javier, Temme, Nico C.

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Properties satisfied by the moments of the partial non-central $χ$ -square distribution function, also known as Nuttall Q-functions, and methods for computing these moments are discussed in this paper. The Nuttall Q-function is involved in the study of a variety of problems in different fields, as for example digital communications.