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Infinite family of approximations of the Digamma function

✍ Scribed by Isa Muqattash; Mohammed Yahdi

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
184 KB
Volume
43
Category
Article
ISSN
0895-7177

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✦ Synopsis

The aim of this work is to find "good" approximations to the Digamma function Ψ . We construct an infinite family of "basic" functions {I a , a ∈ [0, 1]} covering the Digamma function. These functions are shown to approximate Ψ locally and asymptotically, and it is shown that for any x ∈ R + , there exists an a such that Ψ (x) = I a (x). Local and global bounding error functions are found and, as a consequence, new inequalities for the Digamma function are introduced. The approximations are compared to another, well-known, approximation of the Digamma function and we show that an infinite number of members of the family are better.

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