# Mathematica: numerical non-evaluation of special functions

1. Apr 16, 2012

### muppet

Hi all,
I've been getting Mathematica to do some integrals for me, which are typically returning sums of Meijer-G functions. When I try and obtain numerical values for these sums, some of my results have contained terms which Mathematica has refused to evaluate numerically; an example is
MeijerG[{{}, {}}, {{1, 7/6, 4/3, 4/3, 3/2, 5/3, 11/6}, {0, 5/6, 7/6, 4/3, 3/2, 5/3, 11/6}}, 0]

Inside a N[], Mathematica just spits back
N[%]= MeijerG[{{}, {}}, {{1., 1.16667, 1.33333, 1.33333, 1.5, 1.66667, 1.83333}, {0., 0.833333, 1.16667, 1.33333, 1.5, 1.66667, 1.83333}}, 0.]

A plot of the (real and imaginary parts of the) function
MeijerG[{{}, {}}, {{1, 7/6, 4/3, 4/3, 3/2, 5/3, 11/6}, {0, 5/6, 7/6, 4/3, 3/2, 5/3, 11/6}}, x]
suggests that it vanishes at the origin, and its limit as x->0 is zero. But the test PossibleZeroQ, applied to this function at zero argument, yields the result "False".

If anyone could explain to me what's going on here, I'd be grateful.

2. Apr 17, 2012

### muppet

Update: when I tried to create a table of these results, I got an error message I didn't get yesterday:
N::meprec: Internal precision limit \$ MaxExtraPrecision=50`. reached whilst evaluating MeijerG[...].

(Why it would helpfully tell me this today but not yesterday I have no idea, but never mind.)

It looks as if this value is indeed zero, which somehow upsets Mathematica's idea of precision, so I'm recreating my table now using the command Quiet[N[MeijerG[...]]]. I'll be back if that doesn't work, but otherwise thanks to all who read this.

3. Apr 17, 2012

### muppet

In my previous post I forgot that the problematic expression was the result of doing an integral, so the output to my table was still given as a number plus this complicated way of writing zero; it also gives the absolute value of each entry formally in terms of this abomination, rather than as a number. Does anyone know a way of preventing this from happening?

4. Apr 22, 2012

### djelovin

For some choices of parameters MeijerG is not defined! Try posting whole integral.