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►Spenceley and Spenceley (1947) tabulates , , , , for and to 12D, or 12 decimals of a radian in the case of .
►Curtis (1964b) tabulates , , for , , and (not ) to 20D.
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►Zhang and Jin (1996, p. 678) tabulates , , for and to 7D.
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►Figure 22.4.1 illustrates the locations in the -plane of the poles and zeros of the three principal Jacobian functions in the rectangle with vertices , , , .
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►This half-period will be plus or minus a member of the triple ; the other two members of this triple are quarter periods of .
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Table 22.4.3: Half- or quarter-period shifts of variable for the Jacobian elliptic functions.
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►They are algebraic functions of , , and , and have primitive period .
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►Lamé–Wangerin functions are solutions of (29.2.1) with the property that is bounded on the line segment from to .
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►►►Figure 19.3.1:
and as functions of for .
Graphs of and are the mirror images in the vertical line .
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►Figure 19.3.5:
as a function of and for , .
…As it has the limit .
If , then it reduces to .
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Magnify3DHelp
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►Figure 19.3.12:
as a function of complex for , .
…On the upper edge of the branch cut () it has the (negative) value , with limit 0 as .
Magnify3DHelp
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►Minimax polynomial approximations (§3.11(i)) for and in terms of with can be found in Abramowitz and Stegun (1964, §17.3) with maximum absolute errors ranging from 4×10⁻⁵ to 2×10⁻⁸.
Approximations of the same type for and for are given in Cody (1965a) with maximum absolute errors ranging from 4×10⁻⁵ to 4×10⁻¹⁸.
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