Difference between revisions of "2F1(1/2,1;3/2;z^2)=log((1+z)/(1-z))/(2z)"
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(Created page with "==Theorem== The following formula holds: $${}_2F_1 \left( \dfrac{1}{2}, 1 ; \dfrac{3}{2}; z^2 \right)= \dfrac{1}{2z} \log \left( \dfrac{1+z}{1-z} \right),$$ where ${}_2F_1$ de...") |
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=2F1(1,1;2;z)=-log(1-z)/z|next=2F1(1/2,1;3/2;-z^2)=arctan(z)/z}}: 15.1.4 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=2F1(1,1;2;z)=-log(1-z)/z|next=2F1(1/2,1;3/2;-z^2)=arctan(z)/z}}: $15.1.4$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 23:16, 12 July 2016
Theorem
The following formula holds: $${}_2F_1 \left( \dfrac{1}{2}, 1 ; \dfrac{3}{2}; z^2 \right)= \dfrac{1}{2z} \log \left( \dfrac{1+z}{1-z} \right),$$ 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): $15.1.4$
