Thermodynamic quantities for the Klein-Gordon equation with a linear plus inverse-linear potential: Biconfluent Heun functions

We study some thermodynamic 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 from the biconfluent Heun's equation. We use a method based on the Euler-MacLaurin formula to analytically compute the thermal functions by considering only the contribution of positive part of the spectrum to the partition function.