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{\displaystyle K=\prod _{k=1}^{\infty }{\left(1+{1 \over k^{2}+2k}\right)}^{\log _{2}k}=\prod _{k=1}^{\infty }k^{\log _{2}^{}\left(1+{1 \over k^{2}+2k}\right)}}
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{\displaystyle K=\prod _{k=1}^{\infty }{\left(1+{1 \over k(k+2)}\right)}^{\log _{2}k}=\prod _{k=1}^{\infty }{\left(1+{1 \over k(k+2)}\right)}^{{lnk} \over {ln2}}}
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{\displaystyle K={{1} \over {\log(2)}}\sum _{s=1}^{\infty }{{\zeta (2s)-1} \over {s}}\sum _{k=1}^{2s-1}{{-1^{(k+1)}} \over {k}}}
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{\displaystyle K=exp\left({{1} \over {ln2}}\sum _{k=1}^{\infty }{{H_{2k-1}^{'}(\zeta (2k)-1)} \over {k}}\right)}
H
{\displaystyle H}
조화수 ,
ζ
{\displaystyle \zeta }
리만 제타 함수
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{\displaystyle \log(K_{0})={{1} \over {\log(2)}}\sum _{s=1}^{\infty }{{\zeta (2s)-1} \over {s}}\sum _{k=1}^{2s-1}{{-1^{(k+1)}} \over {k}}}
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{\displaystyle \log(K_{0}){\log(2)}=\sum _{s=1}^{\infty }{{\zeta (2s)-1} \over {s}}\sum _{k=1}^{2s-1}{{-1^{(k+1)}} \over {k}}}
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{\displaystyle \log(K_{0}){\log(2)}=\sum _{s=1}^{\infty }{{\zeta (2s)-1} \over {s}}\left({1 \over 1}-{1 \over 2}+{1 \over 3}-\cdots +{1 \over (2s-1)}\right)}
![{\displaystyle K_{p}=\left[\sum _{k=1}^{\infty }-k^{p}\log _{2}\left(1-{{1} \over {(k+1)^{2}}}\right)\right]^{1 \over p}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ad1e90934f2ce04bf62283477804060122fd8060)
![{\displaystyle \;\;\;=\left[{{1} \over {ln2}}\sum _{k=1}^{\infty }k^{p}ln\left(1+{{1} \over {k(k+2)}}\right)\right]^{1 \over p}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f154659c68260b1c87fd22ba6253a40040fa1409)
