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# 4 Inverse Mittag-Leffler functions

[647.7.1] We introduce the inverse generalized Mittag-Leffler functions as the solutions of the equation

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[647.7.2] Our ability to calculate allows us to evaluate also by solving this functional equation numerically. [647.7.3] We have succeeded to determine the principal branch of in such a way that three conditions are fulfilled. [647.7.4] 1. The function is single valued and well defined on its principal branch. [647.7.5] 2. Its principal branch reduces to the principal branch of the logarithm for . [647.7.6] 3. Its principal branch is a simply connected subset of the complex plane. [647.7.7] Figure 15 shows the principal branch for the case , .