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%I #18 Jun 09 2021 06:16:19
%S 0,2,6,0,8,9,6,5,1,7,1,1,5,1,2,9,5,1,0,7,8,1,9,7,9,3,5,9,2,8,9,3,5,5,
%T 5,1,3,9,9,0,7,3,5,4,7,8,3,6,5,7,4,3,9,8,5,9,2,7,0,8,5,1,7,7,5,3,7,9,
%U 0,7,5,3,7,9,0,1,4,6,2,2,9,4,6,0,9,4,8,9,1,7,5
%N Decimal expansion of the torsional rigidity constant for a right isosceles triangular shaft.
%C No closed form is apparently known.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TorsionalRigidity.html">Torsional Rigidity</a>.
%F 1/12 - (16*Sum_{n >= 1}(coth(((-1 + 2*n)*Pi)/2)/(-1 + 2*n)^5))/Pi^5.
%e 0.026089651711512...
%p Digits := 130 ; x := 31*Zeta(5)/32 ; for l from 1 to 70 do x := x+2* hypergeom([1/2,1/2,1/2,1/2,1/2,1],[3/2,3/2,3/2,3/2,3/2],exp(-2*Pi*l))/exp(Pi*l) ; x := evalf(x) ; y := evalf(-16*x/Pi^5+1/12) ; print(y) ; end do: # _R. J. Mathar_, Aug 31 2010
%t digits = 130; x = N[(31*Zeta[5])/32, digits]; For[k = 1, k <= 70, k++, x = x + (2*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2, 1/2, 1}, {3/2, 3/2, 3/2, 3/2, 3/2}, E^(-2*Pi*k)])/E^(Pi*k); y = 1/12 - (16*x)/Pi^5]; Join[{0}, RealDigits[y][[1]]][[1 ;; 91]] (* _Jean-François Alcover_, Oct 25 2012, translated from _R. J. Mathar_'s Maple program *)
%K nonn,cons
%O 0,2
%A _Eric W. Weisstein_, Aug 27 2010
%E More digits from _R. J. Mathar_, Aug 31 2010
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