Approximations for the psi (digamma) function
نویسندگان
چکیده
منابع مشابه
Infinite family of approximations of the Digamma function
The aim of this work is to find “good” approximations to the Digamma function Ψ. We construct an infinite family of “basic” functions {Ia, a ∈ [0, 1]} covering the Digamma function. These functions are shown to approximate Ψ locally and asymptotically, and that for any x ∈ R, there exists a such that Ψ (x) = Ia (x). Local and global bounding error functions are found and, as a consequence, new ...
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Let ψ(x) denote the digamma function, that is, the logarithmic derivative of Euler’s -function. Let q be a positive integer greater than 1 and γ denote Euler’s constant. We show that all the numbers ψ(a/q)+ γ, (a, q)= 1, 1 a q, are transcendental. We also prove that at most one of the numbers γ, ψ(a/q), (a, q)= 1, 1 a q, is algebraic. © 2007 Elsevier Inc. All rights reserved. MSC: primary 11J81...
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Welch & Peers (1963) used a root-information prior to obtain posterior probabilities for a scalar parameter exponential model and showed that these Bayes probabilities had the confidence property to second order asymptotically. An important undercurrent of this indicates that the constant information reparameterization provides location model structure, for which the confidence property ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1967
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-67-99897-3