Class Digamma

java.lang.Object
org.apache.commons.numbers.gamma.Digamma

public final class Digamma extends Object
Digamma function.

It is defined as the logarithmic derivative of the \( \Gamma \) (Gamma) function: \( \frac{d}{dx}(\ln \Gamma(x)) = \frac{\Gamma^\prime(x)}{\Gamma(x)} \).

See Also:
  • Field Details

  • Constructor Details

    • Digamma

      private Digamma()
      Private constructor.
  • Method Details

    • value

      public static double value(double x)
      Computes the digamma function. This is an independently written implementation of the algorithm described in Jose Bernardo, Algorithm AS 103: Psi (Digamma) Function, Applied Statistics, 1976. A reflection formula is incorporated to improve performance on negative values. Some of the constants have been changed to increase accuracy at the moderate expense of run-time. The result should be accurate to within 1e-8. relative tolerance for 0 < x < 1e-5 and within 1e-8 absolute tolerance otherwise.
      Parameters:
      x - Argument.
      Returns:
      digamma(x) to within 1e-8 relative or absolute error whichever is larger.