Zeta Functions
A few examples of what you can ask Wolfram|Alpha about:
Riemann Zeta Function
compute exact values of the zeta function
numerically evaluate zeta near a nontrivial zero
plot the zeta function on the critical line
find a series representations of the zeta function
find a functional equation for the zeta function
Hurwitz Functions
analyze a series for the Hurwitz zeta function
plot the Hurwitz Lerch transcendent
Riemann-Siegel Functions
plot the Riemann-Siegel functions
Other Zeta Functions
evaluate the prime zeta function
find integral representations of the Dirichlet eta function