■ある無限級数(その25)

  1/(1−z)=1+z+z^2+・・・

この導関数と積分は

  1/(1−z)^2=1+2z+3z^2+・・・

  ln(1/(1−z))=z+z^2/2+z^3/3+・・・

 (その17)を補足しておきたい.

===================================

  z/(1−z)=z+z^2+z^3+・・・

  z^n/(1−z^n)=z^n+z^2n+z^3n+・・・

  Σz^n/(1−z^n)=Σ(z^n+z^2n+z^3n+・・・)

=Σkz^k(1−z^k+1)(1−z^k+2)・・・

=Σ(1+z^n)/(1−z^n)・z^(n^2)

===================================