x/(expx-1)=ΣBnx^n/n!

B0=1

Σ(n+1,k)Bk=0

B0=1,B1=-1/2, B2n+1=0

B2=-16,B4=-1/30,B6=1/42,B8=-1/30,B10=5/66,B12=-691/2730,B14=7/6,・・・

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x/(expx-1)=-x/2+ΣB2nx^2n/(2n)!

xcotx=Σ(-1)^nB2n(2x)^2n/(2n)!

Σ(2n+1,2k)2^2kB2k=2n+1

tanx=cotx-2cot2x

1/sinx=cot(x/2)-cot(x)より

xtanx=Σ(1-2^2n)(-1)^nB2n(2x)^2n/(2n)!

Σ(2n,2k)2^2k(1-2^2k)B2k=-2m

x/sinx=1+2Σ(1-2^2n-1)(-1)^nB2nx^2n/(2n)!

x/(expx+1)=x/2+Σ(1-2^2n)B2nx^2n/(2n)!

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