Rogers-Ramanujan continued fraction

Recall that

for |q|<1 in special form

This is expanded into the following polynomial series as

where the coefficients are

c={1, 1, 0, -1, 0, 1, 1, -1, -2, 0, 2, 2, -1, -3, -1, 3, 3, -2, -5, -1, 6, 5, -3,

-8, -2, 8, 7, -5, -12, -2, 13, 12, -7, -18, -4, 18, 16, -11, -26, -5, 27, 24, -14,

-37, -8, 37, 33, -21, -52, -10, 53, 47, -29, -72, -15, 71, 63, -40, -98, -19, 99,

88, -53, -133, -27, 131, 115, -73, -178, -35, 177, 156, -95, -236, -48, 232, 204, -127, -311, . . . }

as in

There is a general form of Rogers-Ramanujan continued fraction. That is,

for |q|<1 in special form

We have several variants of Kn(q).

for |q|<1 and in special form.

We can see a pattern for every four terms respectively.