Certain integral identities for Chebyshev–Hermite polynomials and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e442" altimg="si2.svg"> <mml:mrow> <mml:msub> <mml:mrow/>

In this work, we derive new generalized integral formulas involving the generalized p R q function and products of Chebyshev–Hermite polynomials. The practical relevance of these formulas is illustrated through their application to the derivation of an analytical solution of a partial differential equation governing heat conduction in a solid with a position-dependent heat loss term. The resulting solution provides valuable insight into the thermal behavior of the system under consideration. Finally, an approximate graphical representation of the heat conduction solution is presented and plotted using the mathematical software MATLAB R2016a, enabling a clear visualization of the obtained results.