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This paper deals with the complete integral of the second kindapproximated by the weighted Hölder mean. In general, there are two ways to be considered. One is to find the best exponential parameters with a given weight, and the other is to find the optimal weights with a given exponential order. The second method will be used in this paper where we find the sharp weighted Hölder mean bounds forin a sense of weight. As a result, we also provide a new method to find the optimal Hölder mean bounds for.

Sharp weighted Hölder mean bounds for the complete elliptic integral of the second kind