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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/09.24.03.0033.01









  


  










Input Form





Derivative[0, 8][JacobiAmplitude][z, 1] == (1/2147483648) Sech[z]^8 (2016 z (-846574260 + 17801835 z^2 - 4250076 z^4 + 231136 z^6) Cosh[z] - 28 z (39183167835 - 138963600 z^2 + 9650016 z^4 + 12573952 z^6) Cosh[3 z] + 32 z (-13568817465 - 345628500 z^2 + 47006064 z^4 + 806368 z^6) Cosh[5 z] - 32 z (2933497035 + 146896050 z^2 + 1082844 z^4 + 1408 z^6) Cosh[7 z] - 4 z (1894043655 + 41380920 z^2 + 99456 z^4 + 256 z^6) Cosh[9 z] + 84 z (2790165 + 355960 z^2 + 2592 z^4) Cosh[11 z] - 3360 z (486 + 25 z^2) Cosh[13 z] + 1260 z Cosh[15 z] + 2 (92708054145 - 3110860620 z^2 + 5672582160 z^4 - 826836864 z^6 + 66489088 z^8) Sinh[z] - 12 (-30801845235 + 427711410 z^2 - 1401711080 z^4 + 115204544 z^6 + 2588032 z^8) Sinh[3 z] + 4 (65465190945 + 1630969200 z^2 + 1340887800 z^4 + 67623360 z^6 + 278912 z^8) Sinh[5 z] - (-89900762805 - 7263574920 z^2 + 102063360 z^4 + 655872 z^6 + 512 z^8) Sinh[7 z] + 21 (573855975 + 81521280 z^2 + 274400 z^4 + 3328 z^6) Sinh[9 z] - 2520 (76823 + 46153 z^2 + 1584 z^4) Sinh[11 z] + 25200 (58 + 25 z^2) Sinh[13 z] - 2520 Sinh[15 z])










Standard Form





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MathML Form







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





2007-05-02





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