[Jprogramming] Digamma function

[John Randall]

Leigh J. Halliwell wrote:
> Dear Raul and J Forum:
>
> I was aware of the D. operator, and admire the solution.  My only question
> is how accurately D. performs numerical differentiation.  Can I rely on
> it,
> or should I seek numerical methods for deriving the gamma functions?
> Thanks.
>

I would investigate numerical methods.  The D. operator does an excellent
job in simple cases.  However, I assume you are looking for a specific
accuracy, and you need to be sure the method works to that.  Numerical
differentiation is unstable in any case (using a very small value of dx
can make things worse), and the gamma function grows very rapidly.

There is a lot of literature on computing this and other special
functions, and I suggeset you look into it.

Best wishes,

John