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I have a function F whose power series i want to find using Series.

It gives me the result I want, except there is a term of $\pi^4/10800$, and i want it to tell me if the result is Zeta[2]^2/300 or Zeta[4]/120. Is there a way to force the Zeta function to not evaluate?

F[x] = Integrate[Binomial[x, k], {k, 0, x}];
Series[F[x], {x, 0, 3}] // TeXForm

$x+\frac{\pi ^2 x^3}{36}+O\left(x^4\right)$

I want the output to be $x+x^3\frac{\zeta(2)}{6}$ instead.

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1 Answer 1

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You could Block Zeta so that it doesn't evaluate:

Block[{Zeta=Inactive[Zeta]},
    Series[F[x],{x,0,6}]
] //TeXForm

$x+\frac{1}{6} x^3 \operatorname{Zeta}(2,1)-\frac{1}{6} x^4 \operatorname{Zeta}(3)+\frac{1}{60} x^5 \left(\operatorname{Zeta}(2,1)^2+9 \operatorname{Zeta}(4,1)\right)+x^6 \left(-\frac{1}{30} \operatorname{Zeta}(3) \operatorname{Zeta}(2,1)-\frac{2 \operatorname{Zeta}(5)}{15}\right)+O\left(x^7\right)$

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  • $\begingroup$ You could postprocess the result with res /. Inactive[Zeta][s_, 1] :> Inactive[Zeta][s]. $\endgroup$
    – Greg Hurst
    Sep 3, 2018 at 20:52
  • $\begingroup$ Also it's strange Inactive[Zeta] doesn't format in TraditionalForm with ζ. $\endgroup$
    – Greg Hurst
    Sep 3, 2018 at 20:53
  • $\begingroup$ @ChipHurst What about res1=res /. Inactive[Zeta][s_ , 1] :> \[Zeta][s] /. Inactive[Zeta][s_ ] :> \[Zeta][s] ? And if you want to activate it, res1 /.\[Zeta][s_] :> Zeta[s] $\endgroup$
    – theorist
    Sep 4, 2018 at 0:41
  • $\begingroup$ @ChipHurst That seems to have changed. In V12, I get ζ in TraditionalForm for Inactive[Zeta][n]. $\endgroup$
    – Michael E2
    Oct 4, 2019 at 10:57

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