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http://functions.wolfram.com/07.23.03.bchz.01
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Hypergeometric2F1[-(35/8), -(23/8), 21/4, z] ==
(16 2^(1/4) (4680 - 88200 z + 913005 z^2 - 8260278 z^3 + 659138067 z^4 +
1844448548 z^5 + 1082960419 z^6 + 128672890 z^7 - 24395 z^8 +
(1/Sqrt[1 - z]) (4 (-1170 + 22635 z - 239130 z^2 + 2176512 z^3 +
67555206 z^4 + 48834698 z^5 - 78042966 z^6 - 38476160 z^7 -
1854020 z^8 + 24395 z^9))))/(14934083745 (1 + Sqrt[1 - z])^(1/4) z^4)
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<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> <mrow> <mo> - </mo> <mfrac> <mn> 35 </mn> <mn> 8 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 23 </mn> <mn> 8 </mn> </mfrac> </mrow> </mrow> <mo> ; </mo> <mfrac> <mn> 21 </mn> <mn> 4 </mn> </mfrac> <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[RowBox[List["-", FractionBox["35", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["23", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["21", "4"], 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> <mn> 16 </mn> <mo> ⁢ </mo> <mroot> <mn> 2 </mn> <mn> 4 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - 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</mo> <mrow> <mn> 1854020 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 38476160 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 78042966 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 48834698 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 67555206 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2176512 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 239130 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 22635 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 1170 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 4680 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 14934083745 </mn> <mo> ⁢ </mo> <mroot> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - 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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["35", "8"]]], ",", RowBox[List["-", FractionBox["23", "8"]]], ",", FractionBox["21", "4"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["16", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["4680", "-", RowBox[List["88200", " ", "z"]], "+", RowBox[List["913005", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["8260278", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["659138067", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1844448548", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["1082960419", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["128672890", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["24395", " ", SuperscriptBox["z", "8"]]], "+", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1170"]], "+", RowBox[List["22635", " ", "z"]], "-", RowBox[List["239130", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2176512", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["67555206", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["48834698", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["78042966", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["38476160", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["1854020", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["24395", " ", SuperscriptBox["z", "9"]]]]], ")"]]]], SqrtBox[RowBox[List["1", "-", "z"]]]]]], ")"]]]], RowBox[List["14934083745", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["z", "4"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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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,...,ap},{b1,...,bq},z] | |
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