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A180314 Decimal expansion of the torsional rigidity constant for a right isosceles triangular shaft. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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, TorsionalRigidity

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-Fran├žois 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

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Last modified January 24 19:19 EST 2020. Contains 331211 sequences. (Running on oeis4.)