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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/09.24.03.0032.01









  


  










Input Form





Derivative[0, 7][JacobiAmplitude][z, 1] == (1/536870912) (Sech[z]^7 (34073202240 z - 1013947200 z^3 + 197756160 z^5 - 12056576 z^7 + 8 z (6658689555 - 113929200 z^2 + 13115424 z^4 + 1349504 z^6) Cosh[2 z] - 4 z (-6182430345 - 98552160 z^2 + 22732416 z^4 + 184832 z^6) Cosh[4 z] + 4 z (1527136695 + 77437080 z^2 + 498624 z^4 + 256 z^6) Cosh[6 z] + 672 z (835245 + 25110 z^2 + 136 z^4) Cosh[8 z] - 1260 z (10951 + 936 z^2) Cosh[10 z] + 56700 z Cosh[12 z] + 7 (-1880382285 + 91432800 z^2 - 107246400 z^4 + 11094016 z^6) Sinh[2 z] - 7 (1869500115 - 12252600 z^2 + 51792000 z^4 + 1816064 z^6) Sinh[4 z] + 21 (-263197425 - 16492800 z^2 + 310560 z^4 + 2048 z^6) Sinh[6 z] - 28 (31327965 + 4828500 z^2 + 50160 z^4 + 64 z^6) Sinh[8 z] + 315 (39353 + 18848 z^2 + 288 z^4) Sinh[10 z] - 315 (211 + 40 z^2) Sinh[12 z] + 45 Sinh[14 z]))










Standard Form





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MathML Form







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Rule Form





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





2007-05-02





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