]> $$K_1\left(x\right)-\ln \left(x\right)I_1\left(x\right)-1=xR\left(x^2\right);I_1\left(x\right)=\frac{x}{2}\left(1+\frac{1}{2}[\frac{x}{2}{]}^2+[\frac{x}{2}{]}^{4}R\left([\frac{x}{2}{]}^2\right)\right);x<1$$