Thermodynamics Quantities for the Klein-Gordon Equation with a Linear plus Inverse-linear Potential: Biconfluent Heun functions

We study some thermodynamics quantities for the Klein-Gordon equation with a linear plus inverse-linear, scalar potential. We obtain the energy eigenvalues with the help of the quantization rule coming from the biconfluent Heun's equation. We use a method based on the Euler-MacLaurin formula to compute the thermal functions analytically by considering only the contribution of positive part of spectrum to the partition function.