Logarithmic Generalization of the Lambert W function and its Applications to Adiabatic Thermostatics 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.Comment: arXiv admin note: text overlap with arXiv:1210.5499 by other author

Asymptotic Estimates for Second Kind Generalized Stirling Numbers

Asymptotic formulas for the generalized Stirling numbers of the second kind with integer and real parameters are obtained and ranges of validity of the formulas are established. The generalizations of Stirling numbers considered here are generalizations along the line of Hsu and Shuie's unified generalization

Asymptotic Estimates for r

The r-Whitney numbers of the second kind are a generalization of all the Stirling-type numbers of the second kind which are in line with the unified generalization of Hsu and Shuie. In this paper, asymptotic formulas for r-Whitney numbers of the second kind with integer and real parameters are obtained and the range of validity of each formula is established

The Peak of Noncentral Stirling Numbers of the First Kind

We locate the peak of the distribution of noncentral Stirling numbers of the first kind by determining the value of the index corresponding to the maximum value of the distribution