Accurate analytical evaluation of the generalized logarithmic and double Fermi–Dirac and Bose–Einstein functions

The accurate definition and powerful evaluation modeling of the various generalized Fermi–Dirac and Bose–Einstein functions remain a challenging problem in various areas of physics. In this study, we develop a general analytical technique for accurately calculating logarithmic and double Fermi–Dirac and Bose–Einstein functions. The obtaining analytical formulae are established by considering the binomial expansion theorem. The obtained expressions are valid in chemical potential values between ‐∞ <μ <0 and have been designated as explicit form features, high precision, and less computing time. The calculation results are tabularly illustrated to show the consistency of the analytical relations analysis under the effect of parameters. Based on a comprehensive analysis of the results, they are potentially useful in applications to evaluate thermionic emission and astrophysics problems.