Gieseking's constant

트리감마 함수(trigamma function)

\(\psi^{(1)}(z + 1) - \psi^{(1)}(z) =-\frac{1}{z^{2}}\)

\(\psi^{(1)}(\frac{1}{3})-\psi^{(1)}(\frac{4}{3})=9\)

Gieseking's constant

\(\operatorname{Cl}_2(\frac{\pi}{3})=\frac{\sqrt{3}}{12}(\psi^{(1)}(\frac{1}{3})-\psi^{(1)}(\frac{2}{3}))\)

http://mathworld.wolfram.com/GiesekingsConstant.html

http://www.research.att.com/~njas/sequences/A143298

http://www.research.att.com/~njas/sequences/A091518

http://www.wolframalpha.com/input/?i=Gieseking's+constant.

http://www.wolframalpha.com/input/?i=sqrt(3)*(trigamma(1/3)-trigamma(2/3))/12

The Newest Inductee in the Number Hall of Fame

• Colin C. Adams, Mathematics Magazine, Vol. 71, No. 5 (Dec., 1998), pp. 341-349