## Another Mathematica bug

Posted by David Zaslavsky on — EditedMath is hard.

Not for Barbie, but for Mathematica.

I ran into a weird Mathematica bug while trying to evaluate the sum

Split this into three parts. The first one is the well-known expansion of the exponential function

The second is *not* the well-known expansion of the exponential function.

Obviously not, in fact, since if two power series are equal, \(\sum_i a_n z^n = \sum_i b_n z^n\), for an infinite number of points, each of their coefficients have to be equal: \(\forall n,\ a_n = b_n\). (You can show this by taking the difference of the two sides and plugging in a bunch of different values of \(z\).)

I guess Mathematica doesn’t know that.

```
In[1] = Sum[PolyGamma[1, k + 1] z^k/k!, {k, 1, Infinity}]
Out[1] = 1/6(-1 + E^z)Pi^2
```

I had my hopes up for …