5
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The following expression is correctly simplified in versions 7, 10.2, 11.0

 FullSimplify[Exp[(9 Zeta[3]^(1/3) n^(2/3))/(4 Log[8]^(2/3)) + (3 c Log[4] Zeta[3]^(1/3) n^(1/3))/(2 Log[8]^(2/3)) - (c^2 Log[4]^2 Zeta[3]^(1/3))/(4 Log[8]^(2/3))] /. c -> ((1 - Log[2]) (3 Zeta[3])^(1/3))/(4  Log[2]^(5/3)), n > 0]

 (* E^(-((Zeta[3]^(1/3) (-36 n^(2/3) Log[2]^(4/3) + 12 n^(1/3) (-1 + Log[2]) Log[2]^(2/3) (3 Zeta[3])^(1/3) + (-1 + Log[2])^2 (3 Zeta[3])^(2/3)))/(16 3^(2/3) Log[2]^2))) *)

but in version 11.3 I get an error message

 (* FullSimplify::infd: Expression 4 n^(1/3) (-3 n^(1/3) Log[2]^(4/3) (3 Zeta[3])^(1/3)-(Log[8] Zeta[3])^(2/3)+Log[2] (Log[8] Zeta[3])^(2/3)) simplified to Indeterminate. *)

Why ? There is no reason for such message.

With Simplify instead FullSimplify is the calculation (in 11.3) correct (with a little longer output).

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3
  • $\begingroup$ I get no errors on 10.4.1 for Microsoft Windows (64-bit), nor on 11.0.1 for Linux x86 (64-bit). $\endgroup$ Jun 20, 2018 at 17:53
  • $\begingroup$ I get Indeterminate on MMA 11.2 Win7-64 $\endgroup$
    – MarcoB
    Jun 20, 2018 at 18:18
  • $\begingroup$ I also get Indeterminate on 11.1.1, Win10-64 $\endgroup$ Jun 20, 2018 at 21:59

1 Answer 1

2
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$Version

(* "11.3.0 for Mac OS X x86 (64-bit) (March 7, 2018)" *)

Using Simplify rather than FullSimplify

f[n_] = Simplify[
  Exp[(9 Zeta[3]^(1/3) n^(2/3))/(4 Log[8]^(2/3)) + (3 c Log[
         4] Zeta[3]^(1/3) n^(1/3))/(2 Log[8]^(2/3)) - (c^2 Log[4]^2 Zeta[
          3]^(1/3))/(4 Log[8]^(2/3))] /. 
   c -> ((1 - Log[2]) (3 Zeta[3])^(1/3))/(4 Log[2]^(5/3))]


(* E^(-((Zeta[3]^(
  1/3) (-144 n^(2/3) Log[2]^(10/3) + 
    24 n^(1/3) (-1 + Log[2]) Log[2]^(5/3) Log[4] (3 Zeta[3])^(
     1/3) + (1 + Log[2]^2 - Log[4]) Log[4]^2 (3 Zeta[3])^(2/3)))/(
 64 Log[2]^(10/3) Log[8]^(2/3)))) *)

Some alternate forms are

f2[n_] = f[n] // ExpandAll // FullSimplify

(* 2^(-((n^(1/3) (-1 + Log[2]) (3 Zeta[3])^(2/3))/(
  4 Log[2]^(7/3)))) E^(-(((-1 + Log[2])^2 Zeta[3])/(16 Log[2]^2)) + (
  3 n^(2/3) (3 Zeta[3])^(1/3))/(4 Log[2]^(2/3))) *)

or

f3[n_] = f[n] // ExpandAll // PowerExpand // Simplify

(* E^(((-1 - Log[2]^2 + Log[4]) (3/Log[8])^(2/3) Zeta[3] + 
 12 n^(2/3) Log[2]^(2/3) (3 Zeta[3])^(1/3) - 
 4 n^(1/3) (Log[2] (3 Zeta[3])^(2/3) - 
    3 3^(1/3) ((Log[2] Zeta[3])/Log[8])^(2/3)))/(16 Log[2]^(4/3))) *)

or

f4[n_] = f[n] // ExpToTrig // Simplify

(* Cosh[(1/(64 Log[2]^(10/3) Log[8]^(2/3)))
  Zeta[3]^(1/
    3) (-144 n^(2/3) Log[2]^(10/3) + 
     24 n^(1/3) (-1 + Log[2]) Log[2]^(5/3) Log[4] (3 Zeta[3])^(
      1/3) + (1 + Log[2]^2 - Log[4]) Log[4]^2 (3 Zeta[3])^(2/3))] - 
 Sinh[(1/(64 Log[2]^(10/3) Log[8]^(2/3)))
  Zeta[3]^(1/
    3) (-144 n^(2/3) Log[2]^(10/3) + 
     24 n^(1/3) (-1 + Log[2]) Log[2]^(5/3) Log[4] (3 Zeta[3])^(
      1/3) + (1 + Log[2]^2 - Log[4]) Log[4]^2 (3 Zeta[3])^(2/3))] *)

All of these expressions are equivalent to the result that you provided from earlier versions

f[n] == f2[n] == f3[n] == f4[n] == 
  E^(-((Zeta[3]^(1/3) (-36 n^(2/3) Log[2]^(4/3) + 
           12 n^(1/3) (-1 + Log[2]) Log[
              2]^(2/3) (3 Zeta[3])^(1/3) + (-1 + Log[2])^2 (3 Zeta[3])^(2/
               3)))/(16 3^(2/3) Log[2]^2))) // FullSimplify

(* True *)
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