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I have the following code:

FDE[d_, η_] := η^(d + 1)/Gamma[d + 2] + π^2/(6*Gamma[d])*η^(d - 1);
Series[FDE[d/t, 1/η]/FDE[d/t - 1, 1/η], {η, 0, 3}]

The series function just returns me the expression. But when I put in some numeric value of $d,t$, it actually gives me an expansion. Does it imply, there doesn't exist a general expansion for the expression that I am looking at? Any other way of doing that?

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V 12.1.1. Just add FullSimplify to help it

 FDE[d_, η_] := η^(d + 1)/Gamma[d + 2] + π^2/(6*Gamma[d])*η^(d - 1);
 Series[FullSimplify[FDE[d/t, 1/η]/FDE[d/t - 1, 1/η]], {η, 0, 3}]

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Using only Simplify gives, on same system the following

 Series[Simplify[FDE[d/t, 1/η]/FDE[d/t - 1, 1/η]], {η, 0, 3}]

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 FullSimplify[%]

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| improve this answer | |
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  • $\begingroup$ Series[Simplify[FDE[d/t, 1/\[Eta]]/FDE[d/t - 1, 1/\[Eta]]], {\[Eta], 0, 3}] works for me in version 12.0 on Windows 10. $\endgroup$ – user64494 Jun 19 at 4:28
  • $\begingroup$ Something to adjust: FullSimplify[%] outputs $$\frac{t}{\eta (d+t)}+\frac{\pi ^2 d \eta }{3 (d+t)}+\frac{\pi ^4 d^2 \eta ^3 (t-d)}{18 t^2 (d+t)}+O\left(\eta ^4\right). $$ $\endgroup$ – user64494 Jun 19 at 4:44

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