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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/09.24.03.0035.01









  


  










Input Form





Derivative[0, 10][JacobiAmplitude][z, 1] == (-(1/1099511627776)) (Sech[z]^10 (60 z (960755170934475 - 12541133626560 z^2 + 5047067174688 z^4 - 378611515392 z^6 + 16817174528 z^8) Cosh[z] - 60 z (-670184901344385 + 2012536486800 z^2 - 1472601799872 z^4 - 76926124800 z^6 + 16540175360 z^8) Cosh[3 z] + 300 z (63704433212343 + 936659223360 z^2 - 107571721824 z^4 + 21757585152 z^6 + 499297792 z^8) Cosh[5 z] - 20 z (-291923536963905 - 9984229229520 z^2 + 876500345952 z^4 + 28037781504 z^6 + 150906880 z^8) Cosh[7 z] + 20 z (50122724308335 + 2103990139440 z^2 - 684639648 z^4 - 4995072 z^6 + 28672 z^8) Cosh[9 z] + 20 z (3115889546175 - 50866492320 z^2 - 5450947488 z^4 - 13918464 z^6 + 512 z^8) Cosh[11 z] - 1080 z (2523588165 + 483566440 z^2 + 13035008 z^4 + 31104 z^6) Cosh[13 z] + 18900 z (1918833 + 369480 z^2 + 4000 z^4) Cosh[15 z] - 37800 z (3369 + 196 z^2) Cosh[17 z] + 56700 z Cosh[19 z] + (-5159604364407675 + 5478046459200 z^2 - 281744300980800 z^4 + 44507024432640 z^6 - 4825025049600 z^8 + 284316852224 z^10) Sinh[z] - 2 (5512444108203375 + 52403872468500 z^2 + 250898785426800 z^4 - 30435995600640 z^6 + 1703842398720 z^8 + 44457926656 z^10) Sinh[3 z] + 20 (-456326879156127 - 13746266210250 z^2 - 13488971580000 z^4 + 624136423680 z^6 + 68225961600 z^8 + 359698432 z^10) Sinh[5 z] - (4202594639779725 + 248800859420400 z^2 + 46922997492000 z^4 + 3841539206400 z^6 + 52805813760 z^8 + 80580608 z^10) Sinh[7 z] + (-1049340690712125 - 95964233576400 z^2 + 3341533456800 z^4 + 48452947200 z^6 + 14077440 z^8 + 4096 z^10) Sinh[9 z] - 2520 (42037315020 + 4048385535 z^2 - 256959000 z^4 - 3496832 z^6 + 448 z^8) Sinh[11 z] + 5670 (360007785 + 278440340 z^2 + 19053520 z^4 + 186624 z^6) Sinh[13 z] - 2835 (8605849 + 7818800 z^2 + 400000 z^4) Sinh[15 z] + 1587600 (67 + 33 z^2) Sinh[17 z] - 113400 Sinh[19 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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