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

0,2

Comments

No closed form is apparently known.

Links

Table of n, a(n) for n=0..90.

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

Sequence in context: A197035 A227805 A267314 * A065344 A131105 A321713

Adjacent sequences: A180311 A180312 A180313 * A180315 A180316 A180317

Keyword

nonn,cons

Author

Eric W. Weisstein, Aug 27 2010

Extensions

More digits from R. J. Mathar, Aug 31 2010

Status

approved