Rogers-Ramanujan continued fraction

Rogers-Ramanujan identities are

and

where the coefficients of polynomials for G(q) and H(q) are

{1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 10, 12, 14, 17, 19, 23, 26, 31, 35, 41, 46, 54, . . .}

and

{1, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 6, 6, 8, 9, 11, 12, 15, 16, 20, 22, 26, 29, 35, 38, . . .}

Their ratio is known as the original form of Rogers-Ramanujan continued fraction.

That is,

or

for |q|<1 in special form

Another standard form of Rogers-Ramanujan continued fraction is

When we define

we have

in special form