16 Dec
2019
16 Dec
'19
9:59 a.m.
Hi François, Mathematica immediately gives In[152]:= Assuming[x \[Element] Reals, FullSimplify[Pi/2 == Sum[(2*n)!*(1 + x^(4*n + 2))/(2^(2*n)*(n!)^2*(1 + x^4)^(n + 1/2)*(2*n + 1)), {n, 0, \[Infinity]}]]] Out[152]= 2 (ArcCsc[Sqrt[1 + x^4]] + ArcSin[x^2/Sqrt[1 + x^4]]) == \[Pi] but is unable to finish the proof, nor even plot the constant. You have apparently exposed another headache for the developers. —rwg On Mon, Dec 16, 2019 at 6:29 AM françois mendzina essomba2 <m_essob@yahoo.fr> wrote:
Hi,
Pi/2==sum((2*n)!*(1+x^(4*n+2))/(2^(2*n)*(n!)^2*(1+x^4)^(n+1/2)*(2*n+1)) ,n=0..inf);
an identity transformation gives this result for any real number.
I wonder what other process can lead to this formula
Best regards.