■逆数和とその積分表示(その10)

  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)

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[1]H1/2=2−2log2

[2]H1/3=3−π/2√3−3/2・log3

   H2/3=3/2+π/2√3−3/2・log3

[3]H1/4=4−π/2−3・log2

   H3/4=4/2+π/2−3・log2

[4]H1/5=5−5^-1/4πφ^2/3/2−5/4・log5−√5/2・logφ

   H2/5=5/2−5^-1/4πφ^-2/3/2−5/4・log5+√5/2・logφ

   H3/5=5/3+5^-1/4πφ^-2/3/2−5/4・log5+√5/2・logφ

   H4/5=5/4−5^-1/4πφ^2/3/2−5/4・log5−√5/2・logφ

[5]H1/6=6−π√3/2−2・log2−3/2・log3

   H5/6=6/5+π√3/2−2・log2−3/2・log3

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