Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 8 and fixed z and a>0 > For fixed z and a=3, b>=a > For fixed z and a=3, b=6





http://functions.wolfram.com/07.23.03.c9gi.01









  


  








Input Form





Hypergeometric2F1[3, 6, -(27/8), z] == (1/1009854185472) ((1/(-1 + z)^12) (16 (63115886592 - 1094008700928 z + 10189340147712 z^2 - 79155039305728 z^3 + 1159850247585792 z^4 + 4029323419369893 z^5 + 2008139245716088 z^6 + 60563140501248 z^7 - 3636893094912 z^8 + 157697261568 z^9)) + (1/(1 - z)^(99/8)) (5707189407150 (-1)^(1/8) (-1 + (-1)^(3/4)) z^(35/8) (2193 + 4080 z + 1280 z^2) ArcTan[1 - (z^(1/8) Cos[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Sin[Pi/8])/(1 - z)^(1/8))]) + (1/(1 - z)^(99/8)) (5707189407150 (-1)^(1/8) (-1 + (-1)^(3/4)) z^(35/8) (2193 + 4080 z + 1280 z^2) ArcTan[1 + (z^(1/8) Cos[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Sin[Pi/8])/(1 - z)^(1/8))]) - (1/(1 - z)^(99/8)) (5707189407150 (-1)^(3/8) (-1 + (-1)^(1/4)) z^(35/8) (2193 + 4080 z + 1280 z^2) ArcTan[1 - (z^(1/8) Sin[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Cos[Pi/8])/(1 - z)^(1/8))]) - (1/(1 - z)^(99/8)) (5707189407150 (-1)^(3/8) (-1 + (-1)^(1/4)) z^(35/8) (2193 + 4080 z + 1280 z^2) ArcTan[1 + (z^(1/8) Sin[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Cos[Pi/8])/(1 - z)^(1/8))]) - (1/(1 - z)^(99/8)) (2853594703575 (-1)^(3/8) (-1 + (-1)^(1/4)) z^(35/8) (2193 + 4080 z + 1280 z^2) Log[1 + z^(1/4)/(1 - z)^(1/4) - (2 z^(1/8) Cos[Pi/8])/(1 - z)^(1/8)]) + (1/(1 - z)^(99/8)) (2853594703575 (-1)^(3/8) (-1 + (-1)^(1/4)) z^(35/8) (2193 + 4080 z + 1280 z^2) Log[1 + z^(1/4)/(1 - z)^(1/4) + (2 z^(1/8) Cos[Pi/8])/(1 - z)^(1/8)]) + (1/(1 - z)^(99/8)) (2853594703575 (-1)^(1/8) (-1 + (-1)^(3/4)) z^(35/8) (2193 + 4080 z + 1280 z^2) Log[1 + z^(1/4)/(1 - z)^(1/4) - (2 z^(1/8) Sin[Pi/8])/(1 - z)^(1/8)]) - (1/(1 - z)^(99/8)) (2853594703575 (-1)^(1/8) (-1 + (-1)^(3/4)) z^(35/8) (2193 + 4080 z + 1280 z^2) Log[1 + z^(1/4)/(1 - z)^(1/4) + (2 z^(1/8) Sin[Pi/8])/(1 - z)^(1/8)]))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["3", ",", "6", ",", RowBox[List["-", FractionBox["27", "8"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "1009854185472"], RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "12"]], RowBox[List["(", RowBox[List["16", " ", RowBox[List["(", RowBox[List["63115886592", "-", RowBox[List["1094008700928", " ", "z"]], "+", RowBox[List["10189340147712", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["79155039305728", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1159850247585792", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["4029323419369893", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["2008139245716088", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["60563140501248", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["3636893094912", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["157697261568", " ", SuperscriptBox["z", "9"]]]]], ")"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["99", "/", "8"]]]], RowBox[List["(", RowBox[List["5707189407150", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["35", "/", "8"]]], " ", RowBox[List["(", RowBox[List["2193", "+", RowBox[List["4080", " ", "z"]], "+", RowBox[List["1280", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Cos", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Sin", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["99", "/", "8"]]]], RowBox[List["(", RowBox[List["5707189407150", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["35", "/", "8"]]], " ", RowBox[List["(", RowBox[List["2193", "+", RowBox[List["4080", " ", "z"]], "+", RowBox[List["1280", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "+", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Cos", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Sin", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["99", "/", "8"]]]], RowBox[List["(", RowBox[List["5707189407150", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["35", "/", "8"]]], " ", RowBox[List["(", RowBox[List["2193", "+", RowBox[List["4080", " ", "z"]], "+", RowBox[List["1280", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Sin", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Cos", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["99", "/", "8"]]]], RowBox[List["(", RowBox[List["5707189407150", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["35", "/", "8"]]], " ", RowBox[List["(", RowBox[List["2193", "+", RowBox[List["4080", " ", "z"]], "+", RowBox[List["1280", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "+", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Sin", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Cos", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["99", "/", "8"]]]], RowBox[List["(", RowBox[List["2853594703575", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["35", "/", "8"]]], " ", RowBox[List["(", RowBox[List["2193", "+", RowBox[List["4080", " ", "z"]], "+", RowBox[List["1280", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "-", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Cos", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["99", "/", "8"]]]], RowBox[List["(", RowBox[List["2853594703575", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["35", "/", "8"]]], " ", RowBox[List["(", RowBox[List["2193", "+", RowBox[List["4080", " ", "z"]], "+", RowBox[List["1280", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Cos", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["99", "/", "8"]]]], RowBox[List["(", RowBox[List["2853594703575", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["35", "/", "8"]]], " ", RowBox[List["(", RowBox[List["2193", "+", RowBox[List["4080", " ", "z"]], "+", RowBox[List["1280", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "-", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Sin", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["99", "/", "8"]]]], RowBox[List["(", RowBox[List["2853594703575", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["35", "/", "8"]]], " ", RowBox[List["(", RowBox[List["2193", "+", RowBox[List["4080", " ", "z"]], "+", RowBox[List["1280", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Sin", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]], "]"]]]], ")"]]]]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 6 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 27 </mn> <mn> 8 </mn> </mfrac> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;2&quot;], SubscriptBox[&quot;F&quot;, &quot;1&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[&quot;3&quot;, HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[&quot;6&quot;, HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[TagBox[TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;27&quot;, &quot;8&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[&quot;z&quot;, HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] </annotation> </semantics> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 1009854185472 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 99 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mfrac> <mo> &#8290; </mo> <mrow> <mn> 5707189407150 </mn> <mo> &#8290; </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1280 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4080 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2193 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mrow> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> &#960; </mi> <mn> 8 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 8 </mn> </mroot> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> &#960; </mi> <mn> 8 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 8 </mn> </mroot> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 35 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 99 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mfrac> <mo> &#8290; </mo> <mrow> <mn> 5707189407150 </mn> <mo> &#8290; </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1280 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4080 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2193 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> &#960; </mi> <mn> 8 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 8 </mn> </mroot> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> &#960; </mi> <mn> 8 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 8 </mn> </mroot> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 35 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 99 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mfrac> <mo> &#8290; </mo> <mrow> <mn> 5707189407150 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1280 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4080 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2193 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mrow> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> &#960; </mi> <mn> 8 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 8 </mn> </mroot> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> &#960; </mi> <mn> 8 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 8 </mn> </mroot> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 35 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 99 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mfrac> <mo> &#8290; </mo> <mrow> <mn> 5707189407150 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1280 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4080 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2193 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> &#960; </mi> <mn> 8 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 8 </mn> </mroot> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> &#960; </mi> <mn> 8 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 8 </mn> </mroot> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 35 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 99 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mfrac> <mo> &#8290; </mo> <mrow> <mn> 2853594703575 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1280 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4080 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2193 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 4 </mn> </mroot> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> &#960; </mi> <mn> 8 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 8 </mn> </mroot> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 35 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 99 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mfrac> <mo> &#8290; </mo> <mrow> <mn> 2853594703575 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1280 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4080 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2193 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 4 </mn> </mroot> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> &#960; </mi> <mn> 8 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 8 </mn> </mroot> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 35 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 99 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mfrac> <mo> &#8290; </mo> <mrow> <mn> 2853594703575 </mn> <mo> &#8290; </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1280 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4080 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2193 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 4 </mn> </mroot> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> &#960; </mi> <mn> 8 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 8 </mn> </mroot> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 35 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 99 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mfrac> <mo> &#8290; </mo> <mrow> <mn> 2853594703575 </mn> <mo> &#8290; </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1280 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4080 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2193 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 4 </mn> </mroot> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> &#960; </mi> <mn> 8 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 8 </mn> </mroot> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 35 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 12 </mn> </msup> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 157697261568 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3636893094912 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 60563140501248 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2008139245716088 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4029323419369893 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1159850247585792 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 79155039305728 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 10189340147712 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1094008700928 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 63115886592 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='integer'> 3 </cn> <cn type='integer'> 6 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 27 <sep /> 8 </cn> </apply> </list> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 1009854185472 </cn> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 99 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5707189407150 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1280 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4080 </cn> <ci> z </ci> </apply> <cn type='integer'> 2193 </cn> </apply> <apply> <arctan /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <cos /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <sin /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 35 <sep /> 8 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 99 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5707189407150 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1280 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4080 </cn> <ci> z </ci> </apply> <cn type='integer'> 2193 </cn> </apply> <apply> <arctan /> <apply> <plus /> <apply> <times /> <apply> <cos /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <sin /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 35 <sep /> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 99 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5707189407150 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 8 </cn> </apply> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1280 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4080 </cn> <ci> z </ci> </apply> <cn type='integer'> 2193 </cn> </apply> <apply> <arctan /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <sin /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <cos /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 35 <sep /> 8 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 99 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5707189407150 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 8 </cn> </apply> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1280 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4080 </cn> <ci> z </ci> </apply> <cn type='integer'> 2193 </cn> </apply> <apply> <arctan /> <apply> <plus /> <apply> <times /> <apply> <sin /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <cos /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 35 <sep /> 8 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 99 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2853594703575 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 8 </cn> </apply> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1280 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4080 </cn> <ci> z </ci> </apply> <cn type='integer'> 2193 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <cos /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 35 <sep /> 8 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 99 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2853594703575 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 8 </cn> </apply> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1280 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4080 </cn> <ci> z </ci> </apply> <cn type='integer'> 2193 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <cos /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 35 <sep /> 8 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 99 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2853594703575 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1280 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4080 </cn> <ci> z </ci> </apply> <cn type='integer'> 2193 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <sin /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 35 <sep /> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 99 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2853594703575 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1280 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4080 </cn> <ci> z </ci> </apply> <cn type='integer'> 2193 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <sin /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 35 <sep /> 8 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 12 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 157697261568 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3636893094912 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 60563140501248 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2008139245716088 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4029323419369893 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1159850247585792 </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'> 79155039305728 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 10189340147712 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1094008700928 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 63115886592 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["3", ",", "6", ",", RowBox[List["-", FractionBox["27", "8"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[FractionBox[RowBox[List["16", " ", RowBox[List["(", RowBox[List["63115886592", "-", RowBox[List["1094008700928", " ", "z"]], "+", RowBox[List["10189340147712", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["79155039305728", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1159850247585792", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["4029323419369893", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["2008139245716088", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["60563140501248", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["3636893094912", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["157697261568", " ", SuperscriptBox["z", "9"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "12"]], "+", FractionBox[RowBox[List["5707189407150", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["35", "/", "8"]]], " ", RowBox[List["(", RowBox[List["2193", "+", RowBox[List["4080", " ", "z"]], "+", RowBox[List["1280", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Cos", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Sin", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["99", "/", "8"]]]], "+", FractionBox[RowBox[List["5707189407150", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["35", "/", "8"]]], " ", RowBox[List["(", RowBox[List["2193", "+", RowBox[List["4080", " ", "z"]], "+", RowBox[List["1280", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "+", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Cos", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Sin", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["99", "/", "8"]]]], "-", FractionBox[RowBox[List["5707189407150", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["35", "/", "8"]]], " ", RowBox[List["(", RowBox[List["2193", "+", RowBox[List["4080", " ", "z"]], "+", RowBox[List["1280", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Sin", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Cos", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["99", "/", "8"]]]], "-", FractionBox[RowBox[List["5707189407150", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["35", "/", "8"]]], " ", RowBox[List["(", RowBox[List["2193", "+", RowBox[List["4080", " ", "z"]], "+", RowBox[List["1280", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "+", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Sin", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Cos", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["99", "/", "8"]]]], "-", FractionBox[RowBox[List["2853594703575", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["35", "/", "8"]]], " ", RowBox[List["(", RowBox[List["2193", "+", RowBox[List["4080", " ", "z"]], "+", RowBox[List["1280", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "-", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Cos", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["99", "/", "8"]]]], "+", FractionBox[RowBox[List["2853594703575", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["35", "/", "8"]]], " ", RowBox[List["(", RowBox[List["2193", "+", RowBox[List["4080", " ", "z"]], "+", RowBox[List["1280", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Cos", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["99", "/", "8"]]]], "+", FractionBox[RowBox[List["2853594703575", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["35", "/", "8"]]], " ", RowBox[List["(", RowBox[List["2193", "+", RowBox[List["4080", " ", "z"]], "+", RowBox[List["1280", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "-", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Sin", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["99", "/", "8"]]]], "-", FractionBox[RowBox[List["2853594703575", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["35", "/", "8"]]], " ", RowBox[List["(", RowBox[List["2193", "+", RowBox[List["4080", " ", "z"]], "+", RowBox[List["1280", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]], " ", RowBox[List["Sin", "[", FractionBox["\[Pi]", "8"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "8"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["99", "/", "8"]]]]]], "1009854185472"]]]]]


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





2007-05-02