Limit formulas for \(q\)-exponential functions
Basic analogues of two classical limit formulas for the exponential function are deduced. The main motivation is furnished by relating the first formula with the proof of a result on the probability of a \(q\)- random mapping. Two proofs of the main formulas are presented. The first depends upon Euler's fundamental theory of partitions and the second upon the properties of the \(q\)-binomial coefficient.
scientific article; zbMATH DE number 540953