# Simplify $\mu(x)=\frac{a_x}{b_x}$ where $a_x+b_x=a_{x+1}$ & $\sqrt{a_n^2-b_n^2}+1=b_{n+1}$

can you simplify this function $$\mu(x)$$ into elementary functions where $$\mu(x)=\frac{a_x}{b_x}$$ where $$a_{x-1}+b_{x-1}=a_x$$ & $$\sqrt{a_{x-1}^2-b_{n-1}^2}+1=b_n$$

$$a_1=b_1=1$$ $$\mu(1)=1,\mu(2)=2,\mu(3)=\frac{3\sqrt{3}-3}{2},\mu(4)=\frac{\sqrt{353+202\sqrt{3}}-6\sqrt{3}-11}{2},$$ $$\mu(5)=\frac{5+\sqrt{3}+\sqrt{5-2\sqrt{3}}}{1+\sqrt{25+6\sqrt{3}+2\sqrt{5-2\sqrt{3}}}},\dots$$

• Are there some indices $x$ and some $n?$ – user376343 Aug 2 at 21:17