digamma

(rtools/digamma.m)

Function Synopsis

psi = digamma(z,method,debug)

Help text

  psi = digamma(z)   ... Digamma-Function for real argument z.

  digamma(z) = d/dz log(gamma(z)) = gamma'(z)/gamma(z)

  if 'z' is a matrix, then the digamma-function is evaluated for 
  each element. Results may be inaccurate for real arguments < 10 
  which are neither integers nor half-integers.

  psi = digamma(z,method)

  possible values for optional argument 'method': 
    method = 1           : quick asymptotic series expansion (approximate)
    method = 2           : finite recursion for integer values (exact)
    method = 3           : finite recursion for half-integer values (exact)
    method = 4 (default) : automatic selection of 1,2 or 3 for individual
                           elements in z whichever is appropriate.

  see also:  trigamma, gamma, gammaln, gammainc, specfun