A q-Exponential Operator Based on the Derivative of Order 1 and Summation of Bilateral Basic Hypergeometric Series

2025/11/28 by López, Ronald Orozco
#Combinatorics (math.CO) #FOS: Mathematics #Primary 33E15. Secondary 11F27

paper · doi:10.48550/arxiv.2512.03084

Abstract

We use a new q-exponential operator based on the q^±1-derivative \D_q^±1 of order 1 to derive summation formulas for bilateral basic hypergeometric series ₀ψ₁, ₁ψ₁, ₁ψ₂, and ₂ψ₂. In addition, we provide summation formulas for bilateral series whose terms are basic hypergeometric functions.

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