The Factorial Basis method, initially designed for quasi-triangular, shift-compatible factorial bases, provides solutions to linear recurrence equations in the form of definite-sums. This paper extends the Factorial Basis method to its q-analog, enabling its application in q-calculus. We demonstrate the adaptation of the method to q-sequences and its utility in the realm of q-combinatorics. The extended technique is employed to automatically prove established identities and unveil novel ones, particularly some associated with the Rogers-Ramanujan identities.

翻译：阶乘基方法最初专为准三角形、移位兼容的阶乘基设计，能以定和形式求解线性递归方程。本文将阶乘基方法推广至其q-模拟形式，使其能够在q-微积分中应用。我们展示了该方法对q-序列的适配过程及其在q-组合学领域的实用性。这一扩展技术被用于自动证明已有恒等式并揭示新恒等式，特别是与罗杰斯-拉马努金恒等式相关的一些结论。