2
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The following code doesn't yield any results from Mathematica:

Maximize[
  {Beta[1 + 2 n (p - 1)/p, 1 + 2 m (p - 1)/p] Beta[1 + 2 n/p, 1 + 
     2 m/p]/Beta[n + 1, m + 1]^2, 
   n >= 0 && m >= 0 && p == 4}, 
  {n, m}]

Any ideas as to what I'm missing?

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  • 1
    $\begingroup$ I wonder why you put a constraint like p==4. $\endgroup$ – user59583 Dec 30 '18 at 16:49
  • 1
    $\begingroup$ If you try NMaximixe it will give a solution $\endgroup$ – user59583 Dec 30 '18 at 16:50
2
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NMaximize[{Beta[1 + 2 n (p - 1)/p,1 + 2 m (p - 1)/p] Beta[1 + 2 n/p, 1 + 2 m/p]/Beta[n + 1, m + 1]^2 /. p -> 4, n >= 0 && m >= 0 }, {n, m}]
(*{1.1547, {n -> 2.83145*10^6, m -> 4.82625*10^6}}*)
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  • $\begingroup$ Did you plot the function under consideration? $\endgroup$ – user64494 Dec 30 '18 at 21:06
  • $\begingroup$ No, OP only asked for a global maximum. $\endgroup$ – Ulrich Neumann Dec 30 '18 at 21:54

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