■多角数の逆数和(その55)

[1]

  Σ{1/(n+p/q)-1/(n+1)},n=0~

=π/2・cotpπ/q+log2q-2Σcos2pkπ/q・logsinkπ/q  (0<k<q/2)

1/(p/q)-1+1/(1+p/q)-1/2++1/(2+p/q)-1/3+・・・

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[2]

  Hx=Σ(1/n-1/(n+x))   (n=1~)

Hp/q=q/p-π/2・cotpπ/q+log2q+2Σcos2pkπ/q・logsinkπ/q  (0<k<q/2)

1/1-1/(1+p/q)+1/2-1/(2+p/q)+1/3-1/(3+p/q)+・・・

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[雑感] [1]+[2]=q/p

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