the domain value
It returns $(PSI)(x).
| x | digamma(x) |
|---|---|
| integer < 0 | NaN |
| ±0.0 | $(MNPLUSINF) |
| +∞ | +∞ |
| -∞ | NaN |
| NaN | NaN |
const euler = 0.57721_56649_01532_86060_65121L; assert(isClose(digamma(1), -euler)); assert(digamma(+0.) == -real.infinity); assert(digamma(-0.) == +real.infinity); assert(digamma(+real.infinity) == +real.infinity); assert(isNaN(digamma(-1))); assert(isNaN(digamma(-real.infinity)));
Digamma function, $(PSI)(x)
$(PSI)(x), is the logarithmic derivative of the gamma function, $(GAMMA)(x).
$(PSI)(x) = $(SUP d)/dx ln|$(GAMMA)(x)| (the derivative of logGamma(x))