论文信息 - Some inequalitites for the growth of elliptic integrals

Some inequalitites for the growth of elliptic integrals

Growth of the complete elliptic integral ${\cal K} (r)$ near the singularity $r=1$ is studied and new bounds in terms of elementary functions are obtained. In particular, two recent conjectures are solved and various convexity properties of ${\cal K}(r)$ are given.

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