Estimating the polygamma functions for negative integers
Estimating the polygamma functions for negative integers
Abstract The polygamma functions <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>ψ</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>r</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:msup> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> </mml:math> are defined for all <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>x</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>r</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> </mml:math> . In this paper, the concepts of neutrix and neutrix limit are applied to generalize …