Inverse tangent integral

Summary

The inverse tangent integral $\operatorname{Ti}_2$ is the function $x \mapsto \int_0^x \frac{\arctan t}{t} \, dt$. It is the analogue of the dilogarithm built from the arctangent instead of the logarithm. For real $x$ it equals the imaginary part of $\operatorname{Li}_2(ix)$. Its value at $1$ is Catalan's constant.