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February 12, 2026Open Access

On integral representations of q-difference operators and their applications

Key Points

To explore integral representations of q-difference operators and their applications in complex analysis.
Provided integral representations for two q-difference operators.
Unified representations through (p,q)-differential operators.
Introduced a kernel-like function to generate (p,q)-factorials.
Demonstrated the connections between q-difference operators and special functions.
Established the relevance of (p,q)-differential operators in complex domain analyses.

Abstract

Abstract Integral representations of two q -difference operators are provided in terms of special functions arising in the theory of asymptotic solutions to q -difference equations in the complex domain. Both representations are unified through the so-called ( p , q )-differential operator, for which a kernel-like function is provided, generating the sequence of ( p , q )-factorials.

On integral representations of q-difference operators and their applications

Key Points

Abstract

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