A180309 - OEIS

A180309

Decimal expansion of the torsional rigidity constant for a square shaft.

1, 4, 0, 5, 7, 7, 0, 1, 4, 9, 5, 5, 1, 5, 3, 7, 1, 5, 5, 8, 8, 4, 6, 8, 7, 3, 0, 7, 3, 7, 7, 3, 1, 1, 1, 5, 2, 6, 7, 5, 9, 3, 1, 1, 8, 8, 3, 0, 0, 9, 2, 2, 6, 8, 0, 7, 3, 9, 5, 8, 1, 4, 8, 9, 1, 2, 8, 7, 5, 9, 1, 2, 8, 7, 6, 5, 2, 0, 4, 3, 7, 2, 0, 5, 7, 1, 7, 7, 4, 9, 1, 2, 9, 7, 2, 9, 8, 1, 5, 5, 4, 4, 2

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

No closed form is known.

LINKS

Table of n, a(n) for n=0..102.

FORMULA

Equals (1 - (192*Sum_{n>=1} (tanh(((-1 + 2*n)*Pi)/2)/(-1 + 2*n)^5))/Pi^5)/3.

Equals 1/3 - 62*zeta(5)/Pi^5 + (128/Pi^5)*Sum_{n>=1} 1/((2*n-1)^5*(exp((2*n-1)*Pi)+1)). - Hideaki Nagamine, May 05 2026

EXAMPLE

0.14057701495515371558...