Difference between revisions of "2F1(1,1;2;z)=-log(1-z)/z"

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(Created page with "==Theorem== The following formula holds: $${}_2F_1 \left( 1,1 ; 2 ; z \right) = -\dfrac{\log(1-z)}{z},$$ where ${}_2F_1$ denotes the hypergeometric 2F1 and $\log$ denotes...")
 
 
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==References==
 
==References==
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Limit of (1/Gamma(c))*2F1(a,b;c;z) as c approaches -m|next=}}: 15.1.3
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Limit of (1/Gamma(c))*2F1(a,b;c;z) as c approaches -m|next=2F1(1/2,1;3/2;z^2)=log((1+z)/(1-z))/(2z)}}: $15.1.3$
  
 
[[Category:Theorem]]
 
[[Category:Theorem]]
 
[[Category:Unproven]]
 
[[Category:Unproven]]

Latest revision as of 23:15, 12 July 2016

Theorem

The following formula holds: $${}_2F_1 \left( 1,1 ; 2 ; z \right) = -\dfrac{\log(1-z)}{z},$$ where ${}_2F_1$ denotes the hypergeometric 2F1 and $\log$ denotes the logarithm.

Proof

References