■互いに素となる整数(その5)
(その2)を補足.
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1/1^2+1/3^2+1/5^2+1/7^2+1/9^2−・・・=π^2/8
1+1/9+1/25+・・・
=1+1/4+1/9+・・・−1/4(1+1/4+1/9+・・・
=ζ(2)−ζ(2)/4=π^2/8
なお,カタラン定数G:
G=1/1^2−1/3^2+1/5^2−1/7^2+1/9^2−・・・=0.911・・・
2(1/1^2+1/5^2+1/9^2+・・・)=π^2/8+G
2(1/3^2+1/7^2+1/11^2+・・・)=π^2/8−G
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