How to stop evaluation of Zeta with even arguments

Question

It could be a duplicate question. However I could not find much after a huge searching. I have a huge expression in mathematica involving many Zetas. I want not to evaluate the even Zetas which Mathematica does automatically.

This question has been raised before in a slightly different context in here:

Stop the Zeta function from evaluating

However I would like to know if there is any better way to do this.

Code:

exp= c2*Zeta[2]+c3*Zeta[3]+c4*Zeta[4]+c5*Zeta[5];

The expected output would be the same i.e.

c2*Zeta[2]+c3*Zeta[3]+c4*Zeta[4]+c5*Zeta[5]

but Mathematica does

(c2 Pi^2)/6 + (c4 Pi^4)/90 + c3 Zeta[3] + c5 Zeta[5]

Using the Inactive option:

Block[{Zeta = Inactive[Zeta]},c2*Zeta[2] + c3*Zeta[3] + c4*Zeta[4] + c5*Zeta[5]];

c2 Inactive[Zeta][2] + c3 Inactive[Zeta][3] + c4 Inactive[Zeta][4] + c5 Inactive[Zeta][5]

which when I Activate/Replace again gives the same problem. I am not using notebook interface where this solution 'works', I am using mathematica from terminal.

Answer 1

You can use the following code

Unprotect[Zeta]; Zeta[n_] := "Zeta"[n] /; EvenQ[n];

to do what you want on a global level. For example

ex = c2*Zeta[2] + c3*Zeta[3] + c4*Zeta[4] + c5*Zeta[5]

returns an expression that prints the same.

Later, when you want the actual values of the even Zetas use this

ex /. {"Zeta"[n_] :> Sum[1/k^n, {k, Infinity}]} // InputForm

which returns

(c2*Pi^2)/6 + (c4*Pi^4)/90 + c3*Zeta[3] + c5*Zeta[5]