On Tue, Jul 10, 2012 at 7:05 AM, Damon McDougall wrote:
On Tue, Jul 10, 2012 at 12:27:59PM +0200, Fabien Lafont wrote:
> Hello everyone,
>
> I try to plot the digamma function of (1/2 + 1/x) but I'm not sure that I'm
> plotting the good one.
>
> I've tried:
>
> special.polygamma(0, (1/2 + 1/x))
>
> and
>
> special.polygamma(1, (1/2 + 1/x))

You want special.polygamma(0, (1/2 + 1/x)). See
http://docs.scipy.org/doc/scipy/reference/generated/scipy.special.polygamma.html

The number specifies which derivative of the digamma function you want.
Surely you want the 0th derivative?

> But It returns zero division error even when x is in ]0,1]

I think it blows up at x = 0. What is the type of x in your usecase? Is
it an array? If x contains the element 0, you will get a zero
division error. You could try plotting the points explicitly:

from numpy import linspace
from pylab import *

x = linspace(0.5, 2, num=100, endpoint=True)
y = special.polygamma(0, (1/2 + 1/x))
plot(x, y)
show()

You can compare output against this:
http://www.wolframalpha.com/input/?i=digamma%281%2F2+%2B+1%2Fx%29+between+0.5+and+2

Hope this helps.

Another problem might be the "1/2" part, which in python2.x would yield 0 unless one does "from __future__ import division".

Ben Root