Logarithmic Generalization of the Lambert W Function and Its Applications to Adiabatic Thermostatistics of the Three-Parameter Entropy

A generalization of the Lambert W function called the logarithmic Lambert function is found to be a solution to the thermostatics of the three-parameter entropy of classical ideal gas in adiabatic ensembles. The derivative, integral, Taylor series, approximation formula and branches of the function are obtained. The thermostatics are computed and the heat functions are expressed in terms of the logarithmic Lambert function.