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1: 4.14 Definitions and Periodicity
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4.14.4
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4.14.5
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►The functions and are entire.
In the zeros of are , ; the zeros of are , .
The functions , , , and are meromorphic, and the locations of their zeros and poles follow from (4.14.4) to (4.14.7).
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2: 10.29 Recurrence Relations and Derivatives
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►With defined as in §10.25(ii),
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►For results on modified quotients of the form see Onoe (1955) and Onoe (1956).
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3: 4.28 Definitions and Periodicity
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4.28.9
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4.28.11
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4.28.12
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►The functions and have period , and has period .
The zeros of and are and , respectively, .
4: 10.51 Recurrence Relations and Derivatives
5: 10.36 Other Differential Equations
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►The quantity in (10.13.1)–(10.13.6) and (10.13.8) can be replaced by if at the same time the symbol in the given solutions is replaced by .
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10.36.1
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10.36.2
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►Differential equations for products can be obtained from (10.13.9)–(10.13.11) by replacing by .
6: 22.13 Derivatives and Differential Equations
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Table 22.13.1: Derivatives of Jacobian elliptic functions with respect to variable.
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22.13.7
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22.13.10
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7: 7.4 Symmetry
8: 22.10 Maclaurin Series
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§22.10(i) Maclaurin Series in
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22.10.4
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22.10.5
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22.10.8
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