Optimal Mittag–Leffler Summation

A novel method of an optimal summation is developed that allows for calculating from small-variable asymptotic expansions the characteristic amplitudes variables tending to infinity. The in two versions, as self-similar Borel–Leroy or Mittag–Leffler summations. It based on optimized iterated roots approximants applied and Mittag–Leffler- transformed series with subsequent inverse transformations. As a result, simple transparent expressions critical are obtained explicit form. control parameters come into play They determined optimization procedure, either minimal derivative difference conditions, imposed analytically expressed amplitudes. After diff-log transformation, virtually same procedure can be indices at results number various examples. examples vary rapid growth coefficients fast decay, well intermediate cases. methods give good estimates large-variable exponents. works uniformly wider variety