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JacobiAmplitude






Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiAmplitude[z,m] > Specific values > Specialized values > Derivatives with respect to m > For m==1





http://functions.wolfram.com/09.24.03.0031.01









  


  










Input Form





Derivative[0, 6][JacobiAmplitude][z, 1] == (-(1/16777216)) (Sech[z]^6 (360 z (981117 - 32816 z^2 + 4144 z^4) Cosh[z] - 864 z (-229865 - 310 z^2 + 824 z^4) Cosh[3 z] + 57061260 z Cosh[5 z] + 2792640 z^3 Cosh[5 z] + 12288 z^5 Cosh[5 z] + 5960160 z Cosh[7 z] + 186720 z^3 Cosh[7 z] + 384 z^5 Cosh[7 z] - 108360 z Cosh[9 z] - 4320 z^3 Cosh[9 z] + 180 z Cosh[11 z] + (-48694590 + 4667040 z^2 - 3512160 z^4 + 430592 z^6) Sinh[z] + (-87336540 + 4689360 z^2 - 3411360 z^4 - 60672 z^6) Sinh[3 z] + (-48023100 - 1469520 z^2 + 86880 z^4 + 256 z^6) Sinh[5 z] + (-9270135 - 1455120 z^2 - 13920 z^4) Sinh[7 z] + (110655 + 36720 z^2) Sinh[9 z] - 360 Sinh[11 z]))










Standard Form





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MathML Form







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<times /> <cn type='integer'> 360 </cn> <apply> <sinh /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





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