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Inequalities for Jacobian elliptic functions and Gauss lemniscate functions. (English) Zbl 1241.33018

Summary: A new proof of inequalities involving Jacobian elliptic functions and their inverse functions are obtained. Similar results for the Gauss lemniscate functions are also established. Upper bounds for the inverse Jacobian elliptic functions and for the Gauss arc lemniscate functions are derived.

MSC:

33E05 Elliptic functions and integrals
26D15 Inequalities for sums, series and integrals

Software:

DLMF
Full Text: DOI

References:

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