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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/09.24.03.0034.01









  


  










Input Form





Derivative[0, 9][JacobiAmplitude][z, 1] == (-(1/68719476736)) (Sech[z]^9 (-219166390309860 z + 4018881938400 z^3 - 1257474347136 z^5 + 99787355136 z^7 - 4787214336 z^9 + 32 z (-11253659686605 + 130346098155 z^2 - 40569297552 z^4 + 761193216 z^6 + 159058432 z^8) Cosh[2 z] - 4 z (49191077513655 + 342233262000 z^2 - 45079100640 z^4 + 17477176320 z^6 + 169785344 z^8) Cosh[4 z] + 72 z (-942604664715 - 29481335100 z^2 + 3015563040 z^4 + 76515840 z^6 + 186368 z^8) Cosh[6 z] - 8 z (1626311735055 + 76644470700 z^2 + 444742704 z^4 + 1466496 z^6 + 256 z^8) Cosh[8 z] - 72 z (12803092155 + 82926900 z^2 - 6626592 z^4 + 5632 z^6) Cosh[10 z] + 6804 z (5052795 + 825040 z^2 + 14112 z^4) Cosh[12 z] - 1890000 z (183 + 22 z^2) Cosh[14 z] + 691740 z Cosh[16 z] + 63 (1133054482725 - 10868996160 z^2 + 60126039840 z^4 - 8089396736 z^6 + 582413312 z^8) Sinh[2 z] - 9 (-9019729066005 - 104637866760 z^2 - 330406228320 z^4 + 20758863104 z^6 + 1197604864 z^8) Sinh[4 z] + 81 (557722363275 + 25553168760 z^2 + 8539715520 z^4 + 556510976 z^6 + 4957696 z^8) Sinh[6 z] - 18 (-725821080075 - 64966849920 z^2 + 1306045440 z^4 + 11273472 z^6 + 8192 z^8) Sinh[8 z] + 9 (167613554115 + 20508301800 z^2 - 350232960 z^4 - 2109184 z^6 + 512 z^8) Sinh[10 z] - 189 (141823235 + 99037080 z^2 + 5220000 z^4 + 20736 z^6) Sinh[12 z] + 1890 (138363 + 93624 z^2 + 2000 z^4) Sinh[14 z] - 2835 (275 + 56 z^2) Sinh[16 z] + 315 Sinh[18 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





© 1998- Wolfram Research, Inc.