Amplitude: Specific values (formula 09.24.03.0034)

JacobiAmplitude

$Mathematica Notation$

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

Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox["JacobiAmplitude", TagBox[RowBox[List["(", RowBox[List["0", ",", "9"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["z", ",", "1"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", "68719476736"]]], RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["Sech", "[", "z", "]"]], "9"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "219166390309860"]], " ", "z"]], "+", RowBox[List["4018881938400", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1257474347136", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["99787355136", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["4787214336", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "11253659686605"]], "+", RowBox[List["130346098155", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["40569297552", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["761193216", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["159058432", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]], "-", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["49191077513655", "+", RowBox[List["342233262000", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["45079100640", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["17477176320", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["169785344", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["4", " ", "z"]], "]"]]]], "+", RowBox[List["72", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "942604664715"]], "-", RowBox[List["29481335100", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["3015563040", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["76515840", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["186368", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["6", " ", "z"]], "]"]]]], "-", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["1626311735055", "+", RowBox[List["76644470700", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["444742704", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1466496", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["256", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["8", " ", "z"]], "]"]]]], "-", RowBox[List["72", " ", "z", " ", RowBox[List["(", RowBox[List["12803092155", "+", RowBox[List["82926900", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["6626592", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["5632", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["10", " ", "z"]], "]"]]]], "+", RowBox[List["6804", " ", "z", " ", RowBox[List["(", RowBox[List["5052795", "+", RowBox[List["825040", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["14112", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["12", " ", "z"]], "]"]]]], "-", RowBox[List["1890000", " ", "z", " ", RowBox[List["(", RowBox[List["183", "+", RowBox[List["22", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["14", " ", "z"]], "]"]]]], "+", RowBox[List["691740", " ", "z", " ", RowBox[List["Cosh", "[", RowBox[List["16", " ", "z"]], "]"]]]], "+", RowBox[List["63", " ", RowBox[List["(", RowBox[List["1133054482725", "-", RowBox[List["10868996160", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["60126039840", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["8089396736", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["582413312", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "z"]], "]"]]]], "-", RowBox[List["9", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "9019729066005"]], "-", RowBox[List["104637866760", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["330406228320", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["20758863104", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["1197604864", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["4", " ", "z"]], "]"]]]], "+", RowBox[List["81", " ", RowBox[List["(", RowBox[List["557722363275", "+", RowBox[List["25553168760", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8539715520", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["556510976", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["4957696", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["6", " ", "z"]], "]"]]]], "-", RowBox[List["18", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "725821080075"]], "-", RowBox[List["64966849920", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1306045440", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["11273472", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["8192", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["8", " ", "z"]], "]"]]]], "+", RowBox[List["9", " ", RowBox[List["(", RowBox[List["167613554115", "+", RowBox[List["20508301800", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["350232960", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["2109184", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["512", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["10", " ", "z"]], "]"]]]], "-", RowBox[List["189", " ", RowBox[List["(", RowBox[List["141823235", "+", RowBox[List["99037080", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5220000", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["20736", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["12", " ", "z"]], "]"]]]], "+", RowBox[List["1890", " ", RowBox[List["(", RowBox[List["138363", "+", RowBox[List["93624", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2000", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["14", " ", "z"]], "]"]]]], "-", RowBox[List["2835", " ", RowBox[List["(", RowBox[List["275", "+", RowBox[List["56", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["16", " ", "z"]], "]"]]]], "+", RowBox[List["315", " ", RowBox[List["Sinh", "[", RowBox[List["18", " ", "z"]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> am </mi> <semantics> <mrow> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 9 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", RowBox[List["0", ",", "9"]], ")"]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 68719476736 </mn> </mfrac> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> sech </mi> <mn> 9 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4787214336 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 99787355136 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1257474347136 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4018881938400 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 32 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 159058432 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 761193216 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 40569297552 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 130346098155 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 11253659686605 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 169785344 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 17477176320 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 45079100640 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 342233262000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 49191077513655 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 72 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 186368 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 76515840 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3015563040 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 29481335100 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 942604664715 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 256 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1466496 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 444742704 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 76644470700 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 1626311735055 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 72 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5632 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 6626592 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 82926900 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 12803092155 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 10 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 6804 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 14112 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 825040 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 5052795 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 1890000 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 22 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 183 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 14 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 691740 </mn> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 219166390309860 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 63 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 582413312 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8089396736 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 60126039840 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10868996160 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 1133054482725 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1197604864 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 20758863104 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 330406228320 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 104637866760 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 9019729066005 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 81 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4957696 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 556510976 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8539715520 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 25553168760 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 557722363275 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 18 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8192 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 11273472 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1306045440 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 64966849920 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 725821080075 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 512 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2109184 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 350232960 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 20508301800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 167613554115 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 10 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 189 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 20736 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5220000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 99037080 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 141823235 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 1890 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 93624 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 138363 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 14 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2835 </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> 275 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 315 </mn> <mo> ⁢ </mo> <mrow> <mi> sinh </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 encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 9 </cn> </list> <ci> am </ci> </apply> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 68719476736 </cn> </apply> <apply> <power /> <apply> <sech /> <ci> z </ci> </apply> <cn type='integer'> 9 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -4787214336 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 99787355136 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1257474347136 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4018881938400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 32 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 159058432 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 761193216 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 40569297552 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 130346098155 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -11253659686605 </cn> </apply> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 169785344 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 17477176320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 45079100640 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 342233262000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 49191077513655 </cn> </apply> <apply> <cosh /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 72 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 186368 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 76515840 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3015563040 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 29481335100 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -942604664715 </cn> </apply> <apply> <cosh /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 256 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1466496 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 444742704 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 76644470700 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1626311735055 </cn> </apply> <apply> <cosh /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 72 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 5632 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6626592 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 82926900 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 12803092155 </cn> </apply> <apply> <cosh /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 6804 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 14112 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 825040 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 5052795 </cn> </apply> <apply> <cosh /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1890000 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 22 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 183 </cn> </apply> <apply> <cosh /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 691740 </cn> <apply> <cosh /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 219166390309860 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 63 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 582413312 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8089396736 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 60126039840 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10868996160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 1133054482725 </cn> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 1197604864 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 20758863104 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 330406228320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 104637866760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -9019729066005 </cn> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 81 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4957696 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 556510976 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8539715520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 25553168760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 557722363275 </cn> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 18 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 8192 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11273472 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1306045440 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 64966849920 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -725821080075 </cn> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 512 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2109184 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 350232960 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 20508301800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 167613554115 </cn> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 189 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 20736 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5220000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 99037080 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 141823235 </cn> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1890 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 93624 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 138363 </cn> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2835 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 56 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 275 </cn> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 315 </cn> <apply> <sinh /> <apply> <times /> <cn type='integer'> 18 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox["JacobiAmplitude", TagBox[RowBox[List["(", RowBox[List["0", ",", "9"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["z_", ",", "1"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["Sech", "[", "z", "]"]], "9"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "219166390309860"]], " ", "z"]], "+", RowBox[List["4018881938400", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1257474347136", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["99787355136", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["4787214336", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["32", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "11253659686605"]], "+", RowBox[List["130346098155", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["40569297552", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["761193216", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["159058432", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]], "-", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["49191077513655", "+", RowBox[List["342233262000", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["45079100640", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["17477176320", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["169785344", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["4", " ", "z"]], "]"]]]], "+", RowBox[List["72", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "942604664715"]], "-", RowBox[List["29481335100", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["3015563040", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["76515840", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["186368", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["6", " ", "z"]], "]"]]]], "-", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["1626311735055", "+", RowBox[List["76644470700", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["444742704", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1466496", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["256", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["8", " ", "z"]], "]"]]]], "-", RowBox[List["72", " ", "z", " ", RowBox[List["(", RowBox[List["12803092155", "+", RowBox[List["82926900", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["6626592", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["5632", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["10", " ", "z"]], "]"]]]], "+", RowBox[List["6804", " ", "z", " ", RowBox[List["(", RowBox[List["5052795", "+", RowBox[List["825040", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["14112", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["12", " ", "z"]], "]"]]]], "-", RowBox[List["1890000", " ", "z", " ", RowBox[List["(", RowBox[List["183", "+", RowBox[List["22", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["14", " ", "z"]], "]"]]]], "+", RowBox[List["691740", " ", "z", " ", RowBox[List["Cosh", "[", RowBox[List["16", " ", "z"]], "]"]]]], "+", RowBox[List["63", " ", RowBox[List["(", RowBox[List["1133054482725", "-", RowBox[List["10868996160", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["60126039840", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["8089396736", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["582413312", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "z"]], "]"]]]], "-", RowBox[List["9", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "9019729066005"]], "-", RowBox[List["104637866760", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["330406228320", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["20758863104", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["1197604864", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["4", " ", "z"]], "]"]]]], "+", RowBox[List["81", " ", RowBox[List["(", RowBox[List["557722363275", "+", RowBox[List["25553168760", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8539715520", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["556510976", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["4957696", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["6", " ", "z"]], "]"]]]], "-", RowBox[List["18", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "725821080075"]], "-", RowBox[List["64966849920", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1306045440", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["11273472", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["8192", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["8", " ", "z"]], "]"]]]], "+", RowBox[List["9", " ", RowBox[List["(", RowBox[List["167613554115", "+", RowBox[List["20508301800", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["350232960", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["2109184", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["512", " ", SuperscriptBox["z", "8"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["10", " ", "z"]], "]"]]]], "-", RowBox[List["189", " ", RowBox[List["(", RowBox[List["141823235", "+", RowBox[List["99037080", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5220000", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["20736", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["12", " ", "z"]], "]"]]]], "+", RowBox[List["1890", " ", RowBox[List["(", RowBox[List["138363", "+", RowBox[List["93624", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2000", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["14", " ", "z"]], "]"]]]], "-", RowBox[List["2835", " ", RowBox[List["(", RowBox[List["275", "+", RowBox[List["56", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["16", " ", "z"]], "]"]]]], "+", RowBox[List["315", " ", RowBox[List["Sinh", "[", RowBox[List["18", " ", "z"]], "]"]]]]]], ")"]]]], "68719476736"]]]]]]]

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

2007-05-02