Ramanujan continued fractions of order sixteen

We study the continued fractions I1(τ) and I2(τ) of order sixteen by adopting the theory of modular functions. These functions are analogues of Rogers-Ramanujan continued fraction r(τ) with modularity and many interesting properties. Here we prove the modularities of I1(τ) and I2(τ) to find the relation with the generator of the field of modular functions on F0(16). Moreover we prove that the values 2(I1(τ)2 + 1/I 1(τ)2) and 2(I2(τ)2 + 1/I 2(τ)2) are algebraic integers for certain imaginary quadratic quantity τ.