Amplitude: Specific values (formula 09.24.03.0024)

JacobiAmplitude

$Mathematica Notation$

Derivatives with respect to m

For m==0

http://functions.wolfram.com/09.24.03.0024.01

Input Form

Derivative[0, 9][JacobiAmplitude][z, 0] == (9/268435456) (-103483364040 z + 8 z (-25939014255 + 5555289600 z^2 - 159108096 z^4 + 704512 z^6) Cos[2 z] + 32 z (-1623372345 + 777023520 z^2 - 47394816 z^4 + 262144 z^6) Cos[4 z] - 1008 z (8267935 - 5280000 z^2 + 338688 z^4) Cos[6 z] - 672 z (1420635 - 900480 z^2 + 32768 z^4) Cos[8 z] + 840 z (-93147 + 44000 z^2) Cos[10 z] + 10080 z (-437 + 96 z^2) Cos[12 z] - 153720 z Cos[14 z] - 2520 z Cos[16 z] + 2 (63806773905 - 65048634000 z^2 + 4684162560 z^4 - 55164928 z^6 + 65536 z^8) Sin[2 z] - 896 (-26369730 + 53735895 z^2 - 8736000 z^4 + 188416 z^6) Sin[4 z] - 21 (-154280035 + 429920640 z^2 - 86400000 z^4 + 1327104 z^6) Sin[6 z] + 13440 (26199 - 78822 z^2 + 13312 z^4) Sin[8 z] + 210 (142083 - 377520 z^2 + 32000 z^4) Sin[10 z] - 13440 (-142 + 261 z^2) Sin[12 z] - 1260 (-69 + 56 z^2) Sin[14 z] + 2520 Sin[16 z] + 35 Sin[18 z])

Standard Form

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MathML Form

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</mrow> <mo> - </mo> <mn> 142 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 1260 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 56 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 69 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 14 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2520 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 35 </mn> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 18 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml 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Rule Form

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

2007-05-02