Amplitude: Specific values (formula 09.24.03.0022)

JacobiAmplitude

$Mathematica Notation$

Derivatives with respect to m

For m==0

http://functions.wolfram.com/09.24.03.0022.01

Input Form

Derivative[0, 7][JacobiAmplitude][z, 0] == (1/8388608) (-564490080 z - 336 z (3090765 - 537680 z^2 + 8448 z^4) Cos[2 z] - 168 z (1317345 - 434560 z^2 + 8192 z^4) Cos[4 z] + 7560 z (-3755 + 1248 z^2) Cos[6 z] + 3360 z (-693 + 128 z^2) Cos[8 z] - 113400 z Cos[10 z] - 2520 z Cos[12 z] - 7 (-94986225 + 86129280 z^2 - 4369920 z^4 + 16384 z^6) Sin[2 z] + 2520 (43513 - 70672 z^2 + 6144 z^4) Sin[4 z] + 1890 (6803 - 12752 z^2 + 768 z^4) Sin[6 z] - 20160 (-55 + 84 z^2) Sin[8 z] - 1260 (-53 + 40 z^2) Sin[10 z] + 2520 Sin[12 z] + 45 Sin[14 z])

Standard Form

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MathML Form

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</cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 1248 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -3755 </cn> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 3360 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 128 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -693 </cn> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 113400 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2520 </cn> <apply> <cos /> <apply> <times 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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02