Infinite family of approximations of the Digamma function

Authors:
Isa Muqattash;Mohammed Yahdi
Affiliations:
Department of Mathematics and Computer Science, Ursinus College, 601 E Main Street, Collegeville, PA 19426, USA;Department of Mathematics and Computer Science, Ursinus College, 601 E Main Street, Collegeville, PA 19426, USA
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2006

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Abstract

The aim of this work is to find ''good'' approximations to the Digamma function @J. We construct an infinite family of ''basic'' functions {I"a,a@?[0,1]} covering the Digamma function. These functions are shown to approximate @J locally and asymptotically, and it is shown that for any x@?R^+, there exists an a such that @J(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.