Ramanujan's q-continued fractions and Schroeder-like numbers

TL;DR

This paper explores variants of Ramanujan's q-continued fractions, demonstrating their role as generating functions for q-Schroeder-like numbers, thus connecting classical continued fractions with combinatorial sequences.

Contribution

It introduces new variants of Ramanujan's q-continued fractions and establishes their connection as generating functions for q-Schroeder-like numbers.

Findings

Variants of Ramanujan's q-continued fractions are generating functions for q-Schroeder-like numbers.

Provides simple proofs of Ramanujan's continued fractions.

Establishes a link between continued fractions and combinatorial generating functions.

Abstract

In a recent paper G. Bhatnagar has given simple proofs of some of Ramanujan's continued fractions. In this note we show that some variants of these continued fractions are generating functions of q-Schroeder-like numbers.