Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4jx)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 5 and fixed z

For fixed z and a=6, b>=a

For fixed z and a=6, b=6

http://functions.wolfram.com/07.23.03.b4jx.01

Input Form

Hypergeometric2F1[6, 6, -(22/5), z] == -((4294967296 ((1 - z)^(4/5) - (1 - z)^(3/5) z^(1/5) + (1 - z)^(2/5) z^(2/5) - (1 - z)^(1/5) z^(3/5) + z^(4/5))^15 (-45654296875 + 1104003906250 z - 14146728515625 z^2 + 137382812500000 z^3 - 1344150390625000 z^4 + 28098246093750000 z^5 + 199752045555719608 z^6 + 305618298770545880 z^7 + 145704349748579475 z^8 + 20698292963216750 z^9 + 577982507160625 z^10))/ (45654296875 ((1 - z)^(1/5) + z^(1/5)) (2 (1 - z)^(2/5) + (-1 + Sqrt[5]) (1 - z)^(1/5) z^(1/5) + 2 z^(2/5))^16 (2 (1 - z)^(2/5) - (1 + Sqrt[5]) (1 - z)^(1/5) z^(1/5) + 2 z^(2/5))^16 (-1 + z)^16)) - (1/(1220703125 (1 - z)^(82/5))) (68363568 Sqrt[10 - 2 Sqrt[5]] z^(27/5) (5063968 + 19781125 z + 21385000 z^2 + 7637500 z^3 + 812500 z^4 + 15625 z^5) ArcTan[1 - ((1 - Sqrt[5]) z^(1/5))/(4 (1 - z)^(1/5)), -((Sqrt[5/8 + Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))]) + (1/(1220703125 (1 - z)^(82/5))) (68363568 Sqrt[2 (5 + Sqrt[5])] z^(27/5) (5063968 + 19781125 z + 21385000 z^2 + 7637500 z^3 + 812500 z^4 + 15625 z^5) ArcTan[1 - ((1 + Sqrt[5]) z^(1/5))/(4 (1 - z)^(1/5)), -((Sqrt[5/8 - Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))]) - (1/(1220703125 (1 - z)^(82/5))) (136727136 z^(27/5) (5063968 + 19781125 z + 21385000 z^2 + 7637500 z^3 + 812500 z^4 + 15625 z^5) Log[1 + z^(1/5)/(1 - z)^(1/5)]) + (1/(1220703125 (1 - z)^(82/5))) (34181784 (1 + Sqrt[5]) z^(27/5) (5063968 + 19781125 z + 21385000 z^2 + 7637500 z^3 + 812500 z^4 + 15625 z^5) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)]) - (1/(1220703125 (1 - z)^(82/5))) (34181784 (-1 + Sqrt[5]) z^(27/5) (5063968 + 19781125 z + 21385000 z^2 + 7637500 z^3 + 812500 z^4 + 15625 z^5) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["6", ",", "6", ",", RowBox[List["-", FractionBox["22", "5"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List[RowBox[List["(", RowBox[List["4294967296", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["4", "/", "5"]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "5"]]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "5"]]]]], "+", SuperscriptBox["z", RowBox[List["4", "/", "5"]]]]], ")"]], "15"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "45654296875"]], "+", RowBox[List["1104003906250", " ", "z"]], "-", RowBox[List["14146728515625", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["137382812500000", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1344150390625000", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["28098246093750000", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["199752045555719608", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["305618298770545880", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["145704349748579475", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["20698292963216750", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["577982507160625", " ", SuperscriptBox["z", "10"]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["45654296875", " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]], "+", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "+", RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["2", "/", "5"]]]]]]], ")"]], "16"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "+", RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["2", "/", "5"]]]]]]], ")"]], "16"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "16"]]], ")"]]]]]], "-", RowBox[List[FractionBox["1", RowBox[List["1220703125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["82", "/", "5"]]]]]], RowBox[List["(", RowBox[List["68363568", " ", SqrtBox[RowBox[List["10", "-", RowBox[List["2", " ", SqrtBox["5"]]]]]], " ", SuperscriptBox["z", RowBox[List["27", "/", "5"]]], " ", RowBox[List["(", RowBox[List["5063968", "+", RowBox[List["19781125", " ", "z"]], "+", RowBox[List["21385000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7637500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["812500", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["15625", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "-", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List[SqrtBox[RowBox[List[FractionBox["5", "8"], "+", FractionBox[SqrtBox["5"], "8"]]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["1220703125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["82", "/", "5"]]]]]], RowBox[List["(", RowBox[List["68363568", " ", SqrtBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["5", "+", SqrtBox["5"]]], ")"]]]]], " ", SuperscriptBox["z", RowBox[List["27", "/", "5"]]], " ", RowBox[List["(", RowBox[List["5063968", "+", RowBox[List["19781125", " ", "z"]], "+", RowBox[List["21385000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7637500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["812500", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["15625", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List[SqrtBox[RowBox[List[FractionBox["5", "8"], "-", FractionBox[SqrtBox["5"], "8"]]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", RowBox[List["1220703125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["82", "/", "5"]]]]]], RowBox[List["(", RowBox[List["136727136", " ", SuperscriptBox["z", RowBox[List["27", "/", "5"]]], " ", RowBox[List["(", RowBox[List["5063968", "+", RowBox[List["19781125", " ", "z"]], "+", RowBox[List["21385000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7637500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["812500", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["15625", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "5"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["1220703125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["82", "/", "5"]]]]]], RowBox[List["(", RowBox[List["34181784", " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["27", "/", "5"]]], " ", RowBox[List["(", RowBox[List["5063968", "+", RowBox[List["19781125", " ", "z"]], "+", RowBox[List["21385000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7637500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["812500", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["15625", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "-", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]], "+", FractionBox[SuperscriptBox["z", RowBox[List["2", "/", "5"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", RowBox[List["1220703125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["82", "/", "5"]]]]]], RowBox[List["(", RowBox[List["34181784", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["27", "/", "5"]]], " ", RowBox[List["(", RowBox[List["5063968", "+", RowBox[List["19781125", " ", "z"]], "+", RowBox[List["21385000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7637500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["812500", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["15625", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]], "+", FractionBox[SuperscriptBox["z", RowBox[List["2", "/", "5"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]]], "]"]]]], ")"]]]]]]]]]]

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>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6 </mn> <mo> , </mo> <mn> 6 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 22 </mn> <mn> 5 </mn> </mfrac> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["22", "5"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] </annotation> </semantics> <mo>  </mo> <mrow> <mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 4294967296 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 577982507160625 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 20698292963216750 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 145704349748579475 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 305618298770545880 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 199752045555719608 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 28098246093750000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1344150390625000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 137382812500000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 14146728515625 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1104003906250 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 45654296875 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 4 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <mo> - </mo> <mrow> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 5 </mn> </mroot> </mrow> <mo> + </mo> <msup> <mi> z </mi> <mrow> <mn> 4 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mn> 15 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 45654296875 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 5 </mn> </mroot> <mo> + </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> <mo> ⁢ </mo> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 5 </mn> </mroot> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 16 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> <mo> ⁢ </mo> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 5 </mn> </mroot> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 16 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 16 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 1220703125 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 82 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 68363568 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 10 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 27 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 15625 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 812500 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7637500 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 21385000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 19781125 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 5063968 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </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> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 5 </mn> </mroot> </mrow> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <msqrt> <mrow> <mfrac> <mn> 5 </mn> <mn> 8 </mn> </mfrac> <mo> + </mo> <mfrac> <msqrt> <mn> 5 </mn> </msqrt> <mn> 8 </mn> </mfrac> </mrow> </msqrt> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> </mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 5 </mn> </mroot> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 1220703125 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 82 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 68363568 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> + </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 27 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 15625 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 812500 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7637500 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 21385000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 19781125 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 5063968 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </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> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 5 </mn> </mroot> </mrow> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <msqrt> <mrow> <mfrac> <mn> 5 </mn> <mn> 8 </mn> </mfrac> <mo> - </mo> <mfrac> <msqrt> <mn> 5 </mn> </msqrt> <mn> 8 </mn> </mfrac> </mrow> </msqrt> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> </mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 5 </mn> </mroot> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 1220703125 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 82 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 136727136 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 27 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 15625 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 812500 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7637500 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 21385000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 19781125 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 5063968 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 5 </mn> </mroot> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 1220703125 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 82 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 34181784 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 27 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 15625 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 812500 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7637500 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 21385000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 19781125 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 5063968 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mfrac> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 5 </mn> </mroot> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 1220703125 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 82 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 34181784 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 27 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 15625 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 812500 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7637500 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 21385000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 19781125 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 5063968 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mfrac> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 5 </mn> </mroot> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='integer'> 6 </cn> <cn type='integer'> 6 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 22 <sep /> 5 </cn> </apply> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 4294967296 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 577982507160625 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 20698292963216750 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 145704349748579475 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 305618298770545880 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 199752045555719608 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 28098246093750000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1344150390625000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 137382812500000 </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'> 14146728515625 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1104003906250 </cn> <ci> z </ci> </apply> <cn type='integer'> -45654296875 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 3 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 5 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 2 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 5 </cn> </apply> <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 /> 5 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 4 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> 15 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 45654296875 </cn> <apply> <plus /> <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 /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 2 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <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 /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 5 </cn> </apply> </apply> </apply> <cn type='integer'> 16 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 2 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <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 /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 5 </cn> </apply> </apply> </apply> <cn type='integer'> 16 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 16 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 1220703125 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 82 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 68363568 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 10 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 27 <sep /> 5 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 15625 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 812500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7637500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 21385000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 19781125 </cn> <ci> z </ci> </apply> <cn type='integer'> 5063968 </cn> </apply> <apply> <arctan /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <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 /> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='rational'> 5 <sep /> 8 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </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 /> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 1220703125 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 82 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 68363568 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 27 <sep /> 5 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 15625 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 812500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7637500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 21385000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 19781125 </cn> <ci> z </ci> </apply> <cn type='integer'> 5063968 </cn> </apply> <apply> <arctan /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <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 /> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='rational'> 5 <sep /> 8 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </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 /> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 1220703125 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 82 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 136727136 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 27 <sep /> 5 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 15625 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 812500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7637500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 21385000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 19781125 </cn> <ci> z </ci> </apply> <cn type='integer'> 5063968 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </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 /> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 1220703125 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 82 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 34181784 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 27 <sep /> 5 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 15625 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 812500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7637500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 21385000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 19781125 </cn> <ci> z </ci> </apply> <cn type='integer'> 5063968 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 5 </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'> 2 <sep /> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <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 /> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 1220703125 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 82 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 34181784 </cn> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 27 <sep /> 5 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 15625 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 812500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7637500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 21385000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 19781125 </cn> <ci> z </ci> </apply> <cn type='integer'> 5063968 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 5 </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'> 2 <sep /> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <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 /> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["6", ",", "6", ",", RowBox[List["-", FractionBox["22", "5"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["4294967296", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["4", "/", "5"]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["2", "/", "5"]]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "5"]]]]], "+", SuperscriptBox["z", RowBox[List["4", "/", "5"]]]]], ")"]], "15"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "45654296875"]], "+", RowBox[List["1104003906250", " ", "z"]], "-", RowBox[List["14146728515625", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["137382812500000", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1344150390625000", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["28098246093750000", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["199752045555719608", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["305618298770545880", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["145704349748579475", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["20698292963216750", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["577982507160625", " ", SuperscriptBox["z", "10"]]]]], ")"]]]], RowBox[List["45654296875", " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]], "+", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "+", RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["2", "/", "5"]]]]]]], ")"]], "16"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "+", RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["2", "/", "5"]]]]]]], ")"]], "16"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "16"]]]]]], "-", FractionBox[RowBox[List["68363568", " ", SqrtBox[RowBox[List["10", "-", RowBox[List["2", " ", SqrtBox["5"]]]]]], " ", SuperscriptBox["z", RowBox[List["27", "/", "5"]]], " ", RowBox[List["(", RowBox[List["5063968", "+", RowBox[List["19781125", " ", "z"]], "+", RowBox[List["21385000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7637500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["812500", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["15625", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "-", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List[SqrtBox[RowBox[List[FractionBox["5", "8"], "+", FractionBox[SqrtBox["5"], "8"]]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]]]], "]"]]]], RowBox[List["1220703125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["82", "/", "5"]]]]]], "+", FractionBox[RowBox[List["68363568", " ", SqrtBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["5", "+", SqrtBox["5"]]], ")"]]]]], " ", SuperscriptBox["z", RowBox[List["27", "/", "5"]]], " ", RowBox[List["(", RowBox[List["5063968", "+", RowBox[List["19781125", " ", "z"]], "+", RowBox[List["21385000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7637500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["812500", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["15625", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List[SqrtBox[RowBox[List[FractionBox["5", "8"], "-", FractionBox[SqrtBox["5"], "8"]]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]]]], "]"]]]], RowBox[List["1220703125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["82", "/", "5"]]]]]], "-", FractionBox[RowBox[List["136727136", " ", SuperscriptBox["z", RowBox[List["27", "/", "5"]]], " ", RowBox[List["(", RowBox[List["5063968", "+", RowBox[List["19781125", " ", "z"]], "+", RowBox[List["21385000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7637500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["812500", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["15625", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "5"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]], "]"]]]], RowBox[List["1220703125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["82", "/", "5"]]]]]], "+", FractionBox[RowBox[List["34181784", " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["27", "/", "5"]]], " ", RowBox[List["(", RowBox[List["5063968", "+", RowBox[List["19781125", " ", "z"]], "+", RowBox[List["21385000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7637500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["812500", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["15625", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "-", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]], "+", FractionBox[SuperscriptBox["z", RowBox[List["2", "/", "5"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]]], "]"]]]], RowBox[List["1220703125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["82", "/", "5"]]]]]], "-", FractionBox[RowBox[List["34181784", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["27", "/", "5"]]], " ", RowBox[List["(", RowBox[List["5063968", "+", RowBox[List["19781125", " ", "z"]], "+", RowBox[List["21385000", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7637500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["812500", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["15625", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["5"]]], ")"]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "5"]]]]]], "+", FractionBox[SuperscriptBox["z", RowBox[List["2", "/", "5"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["2", "/", "5"]]]]]], "]"]]]], RowBox[List["1220703125", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["82", "/", "5"]]]]]]]]]]]]

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

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]