Factorial Basis Method for q-Series Applications
CoRR(2024)
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.
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