
psi - digamma and polygamma functions

Calling sequence:

psi(x [ , n ])

Parameter:
x  --   expression
n  --   non-negative integer

Overloading:

1

Summary:

The digamma function is defined as

    psi(x) = diff(ln(gamma(x)), x) = diff(gamma(x), x) / gamma(x)

The polygamma function psi(x,n) is the n-th derivative of the digamma
function, that is diff(psi(x),x$n).  psi returns the function call with
evaluated arguments, if the argument cannot be evaluated to a number. psi
is a kernel function.

>>  psi(2.4);

     0.6529011697

>>  psi(2+I); float(%);

      psi(2+I)

      0.5946503103 + 0.5766740444 I

>>  expand(psi(x+1,2));

                                     - 3
                        psi(x, 2) + 2 x

See also:  gamma

