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
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] > Specific values > For integer and half-integer parameters and fixed z > For fixed z and a1=-5/2, a2>=-5/2 > For fixed z and a1=-5/2, a2=1, a3>=1 > For fixed z and a1=-5/2, a2=1, a3=4 > For fixed z and a1=-5/2, a2=1, a3=4, b1=7/2





http://functions.wolfram.com/07.27.03.abnh.01









  


  










Input Form





HypergeometricPFQ[{-(5/2), 1, 4}, {7/2, 7/2}, -z] == (1/(4194304 z^(5/2))) (19200 Pi^2 - 241280 Sqrt[z] + 144000 Pi^2 z - 1342720 z^(3/2) + 360000 Pi^2 z^2 + 1492176 z^(5/2) + 420000 Pi^2 z^3 + 898800 z^(7/2) + 236250 Pi^2 z^4 + 207900 z^(9/2) + 51975 Pi^2 z^5) + ((2592000 + 41040000 z + 6783774272 z^2 - 8809720160 z^3 + 23195811222 z^4 + 24510819315 z^5 + 33171088551 z^6 + 31509894176 z^7 + 22441255507 z^8 + 12074018438 z^9 + 4880501477 z^10 + 1428758160 z^11 + 272659275 z^12 + 25334775 z^13) Log[1 + Sqrt[z] - Sqrt[1 + z]])/ (141557760 z^2 (1 + z)^(17/2)) + ((-2592000 - 41040000 z - 6783774272 z^2 + 8809720160 z^3 - 23195811222 z^4 - 24510819315 z^5 - 33171088551 z^6 - 31509894176 z^7 - 22441255507 z^8 - 12074018438 z^9 - 4880501477 z^10 - 1428758160 z^11 - 272659275 z^12 - 25334775 z^13) Log[1 - Sqrt[z] + Sqrt[1 + z]])/ (141557760 z^2 (1 + z)^(17/2)) + (5 Sqrt[1 + z] (8224 + 36448 z + 58044 z^2 + 40320 z^3 + 10395 z^4) Log[Sqrt[z] + Sqrt[1 + z]])/(1048576 z^(5/2)) + ((-2592000 - 41040000 z - 6783774272 z^2 + 8809720160 z^3 - 23195811222 z^4 - 24510819315 z^5 - 33171088551 z^6 - 31509894176 z^7 - 22441255507 z^8 - 12074018438 z^9 - 4880501477 z^10 - 1428758160 z^11 - 272659275 z^12 - 25334775 z^13) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])])/(141557760 z^2 (1 + z)^(17/2)) + (1/(1048576 z^(5/2))) (75 (256 + 1920 z + 4800 z^2 + 5600 z^3 + 3150 z^4 + 693 z^5) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (75 (256 + 1920 z + 4800 z^2 + 5600 z^3 + 3150 z^4 + 693 z^5) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/(1048576 z^(5/2)) - (75 (256 + 1920 z + 4800 z^2 + 5600 z^3 + 3150 z^4 + 693 z^5) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/(1048576 z^(5/2))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], ",", "1", ",", "4"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["7", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", RowBox[List["4194304", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["19200", " ", SuperscriptBox["\[Pi]", "2"]]], "-", RowBox[List["241280", " ", SqrtBox["z"]]], "+", RowBox[List["144000", " ", SuperscriptBox["\[Pi]", "2"], " ", "z"]], "-", RowBox[List["1342720", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["360000", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1492176", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["420000", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["898800", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["236250", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["207900", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["51975", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "5"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["2592000", "+", RowBox[List["41040000", " ", "z"]], "+", RowBox[List["6783774272", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["8809720160", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["23195811222", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["24510819315", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["33171088551", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["31509894176", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["22441255507", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["12074018438", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["4880501477", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["1428758160", " ", SuperscriptBox["z", "11"]]], "+", RowBox[List["272659275", " ", SuperscriptBox["z", "12"]]], "+", RowBox[List["25334775", " ", SuperscriptBox["z", "13"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"], "-", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List["141557760", " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["17", "/", "2"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2592000"]], "-", RowBox[List["41040000", " ", "z"]], "-", RowBox[List["6783774272", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8809720160", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["23195811222", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["24510819315", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["33171088551", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["31509894176", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["22441255507", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["12074018438", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["4880501477", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["1428758160", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["272659275", " ", SuperscriptBox["z", "12"]]], "-", RowBox[List["25334775", " ", SuperscriptBox["z", "13"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List["141557760", " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["17", "/", "2"]]]]], ")"]]]], "+", FractionBox[RowBox[List["5", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["8224", "+", RowBox[List["36448", " ", "z"]], "+", RowBox[List["58044", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["40320", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["10395", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["1048576", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2592000"]], "-", RowBox[List["41040000", " ", "z"]], "-", RowBox[List["6783774272", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8809720160", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["23195811222", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["24510819315", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["33171088551", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["31509894176", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["22441255507", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["12074018438", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["4880501477", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["1428758160", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["272659275", " ", SuperscriptBox["z", "12"]]], "-", RowBox[List["25334775", " ", SuperscriptBox["z", "13"]]]]], ")"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], RowBox[List["1", "+", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List["141557760", " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["17", "/", "2"]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["1048576", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], RowBox[List["75", " ", RowBox[List["(", RowBox[List["256", "+", RowBox[List["1920", " ", "z"]], "+", RowBox[List["4800", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5600", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3150", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["693", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], RowBox[List["1", "+", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "]"]]]]]], "+", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List["256", "+", RowBox[List["1920", " ", "z"]], "+", RowBox[List["4800", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5600", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3150", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["693", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", FractionBox["1", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]]]], "]"]]]], RowBox[List["1048576", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List["256", "+", RowBox[List["1920", " ", "z"]], "+", RowBox[List["4800", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5600", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3150", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["693", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", FractionBox["1", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]], "]"]]]], RowBox[List["1048576", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]]]]]]]










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> 3 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 7 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;3&quot;], SubscriptBox[&quot;F&quot;, &quot;2&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;5&quot;, &quot;2&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[&quot;1&quot;, HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[&quot;4&quot;, HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;7&quot;, &quot;2&quot;], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;7&quot;, &quot;2&quot;], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[RowBox[List[&quot;-&quot;, &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> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 4194304 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 51975 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 207900 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 236250 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 898800 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 420000 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1492176 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 360000 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1342720 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 144000 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 241280 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> + </mo> <mrow> <mn> 19200 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 141557760 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 17 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 25334775 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 13 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 272659275 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 12 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1428758160 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4880501477 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 12074018438 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 22441255507 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 31509894176 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 33171088551 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 24510819315 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 23195811222 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8809720160 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6783774272 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 41040000 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2592000 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> - </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 141557760 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 17 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 25334775 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 13 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 272659275 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 12 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1428758160 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4880501477 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 12074018438 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 22441255507 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 31509894176 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 33171088551 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 24510819315 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 23195811222 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8809720160 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 6783774272 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 41040000 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 2592000 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 10395 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 40320 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 58044 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 36448 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 8224 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 1048576 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 141557760 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 17 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 25334775 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 13 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 272659275 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 12 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1428758160 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4880501477 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 12074018438 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 22441255507 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 31509894176 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 33171088551 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 24510819315 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 23195811222 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8809720160 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 6783774272 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 41040000 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 2592000 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 75 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 693 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3150 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5600 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4800 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1920 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 256 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 1048576 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 75 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 693 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3150 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5600 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4800 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1920 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 256 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 1048576 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 75 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 693 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3150 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5600 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4800 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1920 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 256 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 1048576 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> <cn type='integer'> 4 </cn> </list> <list> <cn type='rational'> 7 <sep /> 2 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 4194304 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 51975 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 207900 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 236250 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 898800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 420000 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1492176 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 360000 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1342720 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 144000 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 241280 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 19200 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 141557760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 17 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 25334775 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 13 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 272659275 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 12 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1428758160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4880501477 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12074018438 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 22441255507 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 31509894176 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 33171088551 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 24510819315 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 23195811222 </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'> 8809720160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 6783774272 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 41040000 </cn> <ci> z </ci> </apply> <cn type='integer'> 2592000 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 141557760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 17 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -25334775 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 13 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 272659275 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 12 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1428758160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4880501477 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12074018438 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 22441255507 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 31509894176 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 33171088551 </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'> 24510819315 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 23195811222 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 8809720160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6783774272 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 41040000 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -2592000 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 10395 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 40320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 58044 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 36448 </cn> <ci> z </ci> </apply> <cn type='integer'> 8224 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1048576 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 141557760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 17 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -25334775 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 13 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 272659275 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 12 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1428758160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4880501477 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12074018438 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 22441255507 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 31509894176 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 33171088551 </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'> 24510819315 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 23195811222 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 8809720160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6783774272 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 41040000 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -2592000 </cn> </apply> <apply> <ln /> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 75 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 693 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3150 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1920 </cn> <ci> z </ci> </apply> <cn type='integer'> 256 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ln /> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1048576 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 75 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 693 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3150 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1920 </cn> <ci> z </ci> </apply> <cn type='integer'> 256 </cn> </apply> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1048576 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 75 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 693 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3150 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1920 </cn> <ci> z </ci> </apply> <cn type='integer'> 256 </cn> </apply> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1048576 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], ",", "1", ",", "4"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["7", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["19200", " ", SuperscriptBox["\[Pi]", "2"]]], "-", RowBox[List["241280", " ", SqrtBox["z"]]], "+", RowBox[List["144000", " ", SuperscriptBox["\[Pi]", "2"], " ", "z"]], "-", RowBox[List["1342720", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["360000", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1492176", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["420000", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["898800", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["236250", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["207900", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["51975", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "5"]]]]], RowBox[List["4194304", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2592000", "+", RowBox[List["41040000", " ", "z"]], "+", RowBox[List["6783774272", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["8809720160", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["23195811222", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["24510819315", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["33171088551", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["31509894176", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["22441255507", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["12074018438", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["4880501477", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["1428758160", " ", SuperscriptBox["z", "11"]]], "+", RowBox[List["272659275", " ", SuperscriptBox["z", "12"]]], "+", RowBox[List["25334775", " ", SuperscriptBox["z", "13"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"], "-", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["141557760", " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["17", "/", "2"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2592000"]], "-", RowBox[List["41040000", " ", "z"]], "-", RowBox[List["6783774272", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8809720160", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["23195811222", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["24510819315", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["33171088551", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["31509894176", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["22441255507", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["12074018438", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["4880501477", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["1428758160", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["272659275", " ", SuperscriptBox["z", "12"]]], "-", RowBox[List["25334775", " ", SuperscriptBox["z", "13"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["141557760", " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["17", "/", "2"]]]]]], "+", FractionBox[RowBox[List["5", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["8224", "+", RowBox[List["36448", " ", "z"]], "+", RowBox[List["58044", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["40320", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["10395", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]]]], RowBox[List["1048576", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2592000"]], "-", RowBox[List["41040000", " ", "z"]], "-", RowBox[List["6783774272", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8809720160", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["23195811222", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["24510819315", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["33171088551", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["31509894176", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["22441255507", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["12074018438", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List["4880501477", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["1428758160", " ", SuperscriptBox["z", "11"]]], "-", RowBox[List["272659275", " ", SuperscriptBox["z", "12"]]], "-", RowBox[List["25334775", " ", SuperscriptBox["z", "13"]]]]], ")"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], RowBox[List["1", "+", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "]"]]]], RowBox[List["141557760", " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["17", "/", "2"]]]]]], "+", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List["256", "+", RowBox[List["1920", " ", "z"]], "+", RowBox[List["4800", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5600", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3150", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["693", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], "]"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], RowBox[List["1", "+", SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "]"]]]], RowBox[List["1048576", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List["256", "+", RowBox[List["1920", " ", "z"]], "+", RowBox[List["4800", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5600", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3150", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["693", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", FractionBox["1", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]]]], "]"]]]], RowBox[List["1048576", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List["256", "+", RowBox[List["1920", " ", "z"]], "+", RowBox[List["4800", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5600", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3150", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["693", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", FractionBox["1", RowBox[List[SqrtBox["z"], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]], "]"]]]], RowBox[List["1048576", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]]]]]]]










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





2007-05-02