A Note on an Analogous Continued Fraction of Ramanujan

We give an integral representation for an analogous continued fraction of Ramanujan, for this we first prove an interesting identity.

Adv. in Math. v.41 Ramanujans Lost Notebook III: The Rogers-Ramanujan Continued Fraction Andrews, G.E.
Memoir v.477 The continued fractions found in the Unorganised portions of Ramanujans notebooks Andrews, G.E.;Berndt, B.C.;Jacobsen, L.;Lamphere, R.L.
Quart. J. Math. (Oxford) v.7 Series of Hypergeometric type which are infinite in both directions Bailey, W.N.
Quart. J. Math. (Oxford) v.3 A note on two of Ramanujans formulae Bailey, W.N.
J. Comput. Appl. Math. v.105 The Rogers-Ramanujan continued fraction Berndt, B.C.;Chan, H.H.;Huang, S.S.;Kang, S.;Sohn, J.;Son, S.H.