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Applied Mathematics & Information Sciences

Article Title

Some results on the digamma function

Author Country (or Countries)

Republic of Macedonia

Abstract

The digamma function is defined for $x>0$ as a locally summable function on the real line by $$\psi(x)=-\gamma+\int_0^{\infty}\frac{e^{-t}-e^{-xt}}{1-e^{-t}}\,dt\,.$$ In this paper we use the neutrix calculus to extend the definition for digamma function for the negative integers. Also we consider the derivatives of the digamma function for negative integers.

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