Optimal combinations bounds of root-square and arithmetic means for Toader mean

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Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means (2020, background): “is the complete elliptic integral of the second kind [12,18,30,38,44,50,52] and it is the special case of the Gaussian hypergeometric function [31,41,42,49,57]”