Sqrt(1-z^2)2F1(1,1;3/2;z^2)=arcsin(z)/z

Theorem

The following formula holds: $$\sqrt{1-z^2} {}_2F_1 \left( 1,1 ; \dfrac{3}{2}; z^2 \right)=\dfrac{\arcsin(z)}{z},$$ where ${}_2F_1$ denotes the hypergeometric 2F1 and $\arcsin$ denotes the inverse sine.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous): $15.1.6$