Some functional inequalities for complete elliptic integrals (Q1202754)
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scientific article; zbMATH DE number 109290
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some functional inequalities for complete elliptic integrals |
scientific article; zbMATH DE number 109290 |
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Some functional inequalities for complete elliptic integrals (English)
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3 February 1993
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Let \(K(k)\) and \(E(k)\) be the elliptic integrals of the first and second kind respectively for \(0<k<1\). This paper investigates the monotonicity of functions of the type \[ f(k)=[(1+k^ 2 \varphi(k))E(k)-(1-k^ 2\psi(k))K(k)]/k^ 2 \] for certain functions \(\varphi\) and \(\psi\).
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elliptic integrals
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monotonicity
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