The generalized q-heat equations for q-3D hypergeometric polynomials with applications to generating functions and Askey–Wilson integrals

Key Points

• The generalized q-heat equations describe thermal properties of q-3D hypergeometric polynomials, enhancing understanding of their behavior.
• Key evidence includes various generating functions linked to Askey–Wilson integrals, showing intricate mathematical relationships.
• Analysis of generating functions and integrals forms the basis of new insights into numerical methods for q-3D problems.
• This work may enable advancements in mathematical physics and computational techniques, potentially transforming how we approach complex equations.