What mathematical notation can use for this formula

Question

I just played around with archimedes $\pi$ formula and ended up with

$\pi = \lim\limits_{n \to \infty} 6 \cdot 2^n \cdot \sqrt{2 - \sqrt{2 + \sqrt{2 + ...n times... \sqrt{2 + \sqrt{3}}}}}$

I want to know how to write the nesting $\sqrt{a}$ part as a notation like formula or limit

Does this kind of notation exist?

Answer 1

If you find yourself repeatedly using expressions of this form you could define your own notation. For example (uploading image since MathJax cannot handle the $\LaTeX$)

\left.\sqrt{(a_k+(-1)^{p_k}(}\right\vert_{k=1}^n=\sqrt{(a_1+(-1)^{p_1}\sqrt{(a_2+(-1)^{p_2}\sqrt{(\cdots+\sqrt{a_n}}}}