q-级数应用的阶乘基方法
Factorial Basis Method for q-Series Applications
AI总结：
本文扩展阶乘基方法至q-模拟，应用于q-微积分与q-组合学，自动证明并发现新恒等式，特别是Rogers-Ramanujan相关恒等式。
摘要：
阶乘基方法最初设计用于拟三角、移位相容的阶乘基，以确定和的形式为线性递推方程提供解。本文将阶乘基方法扩展到其q-模拟，使其能够应用于q-微积分。我们展示了该方法对q-序列的适应性及其在q-组合学领域的实用性。扩展技术被用于自动证明已有恒等式并揭示新的恒等式，特别是与Rogers-Ramanujan恒等式相关的一些恒等式。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
