OFFSET
0,2
COMMENTS
No closed form is apparently known.
LINKS
Eric Weisstein's World of Mathematics, Torsional Rigidity.
FORMULA
1/12 - (16*Sum_{n >= 1}(coth(((-1 + 2*n)*Pi)/2)/(-1 + 2*n)^5))/Pi^5.
EXAMPLE
0.026089651711512...
MAPLE
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
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Aug 27 2010
EXTENSIONS
More digits from R. J. Mathar, Aug 31 2010
STATUS
approved