A180314 Decimal expansion of the torsional rigidity constant for a right isosceles triangular shaft.
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, 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, 0, 7, 5, 3, 7, 9, 0, 1, 4, 6, 2, 2, 9, 4, 6, 0, 9, 4, 8, 9, 1, 7, 5
Offset: 0
Examples
0.026089651711512...
Links
- Eric Weisstein's World of Mathematics, Torsional Rigidity.
Programs
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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
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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 *)
Formula
1/12 - (16*Sum_{n >= 1}(coth(((-1 + 2*n)*Pi)/2)/(-1 + 2*n)^5))/Pi^5.
Extensions
More digits from R. J. Mathar, Aug 31 2010
Comments