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JacobiDN






Mathematica Notation

Traditional Notation









Elliptic Functions >JacobiDN[z,m]





Identities involving the group of functions

Cyclic Identities of rank 2

p=3

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General case: (p-1)/2 ∈ Z

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Cyclic Identities of rank 3

p=2

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p=3

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p=4

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General case: pZ

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General case: (p-1)/2 ∈ Z

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Cyclic Identities of rank 4 and above

r=4, p=2

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r=4, p=3

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r=5, p=3

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Local identities of rank 2

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Local identities of rank 3

Rank 3 identities with 3 distinct arguments

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Rank 3 identities with 2 distinct arguments

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Local identities of rank 4

Rank 4 identities with 4 distinct arguments

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Rank 4 identities with 3 distinct arguments

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Rank 4 identities with 2 distinct arguments

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Higher order local identities

Examples of local identities of rank 5

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Local identities of arbitrary rank

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