2F1(1,1;2;z)=-log(1-z)/z

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.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $15.1.3$