A uniform asymptotic expansion for the Jacobian elliptic function sn(u,k) (Q1077652)
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scientific article; zbMATH DE number 3957888
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A uniform asymptotic expansion for the Jacobian elliptic function sn(u,k) |
scientific article; zbMATH DE number 3957888 |
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A uniform asymptotic expansion for the Jacobian elliptic function sn(u,k) (English)
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1986
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The asymptotic behaviour of the function sn(u,k) is considered for \(k\to 1\), uniformly with respect to the parameter u. The method is based on inner and outer expansions and the uniform expansion is obtained by forming a composite expansion and using the matching principle. A numerical comparison is given, where the new expansion is compared with non-uniform expansions from the literature. Results for cn(u,k), dn(u,k) are also given.
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Jacobian elliptic function
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uniform asymptotic expansion
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0.785555362701416
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0.7321807146072388
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