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 | + | * {{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
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $15.1.3$
