Luroth Expansion
Given a real number $x$, this calculator expands it into a Lüroth representation: \[ x = \lfloor x\rfloor + \sum_{n=1}^\infty\left(\prod_{k=1}^{n-1}\frac{1}{d_k(d_k+1)}\right)\frac{1}{d_n+1} =: ((d_0;d_1,d_2,\ldots)) \] where $d_0,d_1,d_2,\ldots$ are integers.