I've got a Mathematica problem that I'm struggling with.
Basically, I've got a complicated expression involving products and sums of Euler Gamma functions, and I'm trying to calculate a series expansion of it. The resulting series expansion includes several factors of Riemann Zeta functions -- derivatives of Gamma yield PolyGamma's (a.k.a., the psi function) and I'm evaluating the series expansion around 1.
Here's the problem. The series expansion yields thousands of terms, and needs to be simplified using Simplify. But, Simplify goes too far for what I need. For example (recall that Zeta[n] ~ pi^n for n even):
a Zeta^2 + b Zeta
Simplifies to something proportional to pi^8. But, I need simplify to stop at the level of the Zeta functions and not simplify further. After it Simplifies, I'm obviously not able to separate pi^8 into its original Zeta^2 and Zeta pieces.
Does anyone have any solutions to this problem -- either through built-in functions or perhaps some creative trick?