Difference between revisions of "Sum of totient equals z/((1-z) squared)"

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==References==
 
==References==
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Sum of totient equals zeta(z-1)/zeta(z) for Re(z) greater than 2|next=}}: $24.3.2 I.B.$
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Sum of totient equals zeta(z-1)/zeta(z) for Re(z) greater than 2|next=Product representation of totient}}: $24.3.2 \mathrm{I}.B.$
  
 
[[Category:Theorem]]
 
[[Category:Theorem]]
 
[[Category:Unproven]]
 
[[Category:Unproven]]

Latest revision as of 04:50, 22 June 2016

Theorem

The following formula holds for $|z|<1$: $$\displaystyle\sum_{k=1}^{\infty} \dfrac{\phi(k)x^k}{1-x^k}= \dfrac{x}{(1-x)^2} ,$$ where $\phi$ denotes the totient.

Proof

References