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In this article, we investigate the bound state solution of the Klein Gordonequation under mixed vector and scalar coupling of an energy-dependent deformedHulth\'en potential in D-dimensions. We obtain a transcendental equation afterwe impose the boundary conditions. We calculate energy spectra in fourdifferent limits and in arbitrary dimension via the Newton-Raphson method.Then, we use a statistical method, namely canonical partition function, anddiscuss the thermodynamic properties of the system in a comprehensive way. Wefind out that some of the thermodynamic properties overlap with each other,some of them do not.

A statistical mechanical analysis on the bound state solution of an energy-dependent deformed Hulth\'en potential energy