The digamma function is the logarithmic derivativeLogarithmically differentiating the Weierstrass product gives
The digamma function is strictly increasing on the positive real axis, whileIt therefore has exactly one positive zero, and that zero lies in .
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The digamma function, denoted as \( \psi(x) \), is the logarithmic derivative of the gamma function \( \Gamma(x) \). Mathematically, it is defined as: \[ \psi(x) = \frac{d}{dx} \ln(\Gamma(x)) = \frac{\Gamma'(x)}{\Gamma(x)} \] where \( \Gamma'(x) \) is the derivative of the gamma function.