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 | | http://functions.wolfram.com/07.23.03.b5rq.01 | 
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 | | Hypergeometric2F1[-(47/8), 45/8, 13/4, z] == 
 (1/(2382000985 z^3)) (4 2^(1/4) (1 + Sqrt[1 - z])^(3/4) 
   (134044 + 2915457 z + 182768994 z^2 - 2568094191 z^3 + 11527353648 z^4 - 
    24430484736 z^5 + 26986856448 z^6 - 15070593024 z^7 + 3369074688 z^8 + 
    (1/Sqrt[1 - z]) (-134044 - 2848435 z - 181294510 z^2 + 2957601621 z^3 - 
      15909017496 z^4 + 42295632960 z^5 - 62716993536 z^6 + 52996079616 z^7 - 
      23931125760 z^8 + 4492099584 z^9))) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["47", "8"]]], ",", FractionBox["45", "8"], ",", FractionBox["13", "4"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2382000985", " ", SuperscriptBox["z", "3"]]]], RowBox[List["(", RowBox[List["4", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List["134044", "+", RowBox[List["2915457", " ", "z"]], "+", RowBox[List["182768994", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2568094191", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["11527353648", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["24430484736", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["26986856448", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["15070593024", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["3369074688", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List[FractionBox["1", SqrtBox[RowBox[List["1", "-", "z"]]]], RowBox[List["(", RowBox[List[RowBox[List["-", "134044"]], "-", RowBox[List["2848435", " ", "z"]], "-", RowBox[List["181294510", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2957601621", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["15909017496", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["42295632960", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["62716993536", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["52996079616", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["23931125760", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["4492099584", " ", SuperscriptBox["z", "9"]]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]] | 
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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> 47 </mn>  <mn> 8 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mfrac>  <mn> 45 </mn>  <mn> 8 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mfrac>  <mn> 13 </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["47", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["45", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["13", "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>  <mfrac>  <mn> 1 </mn>  <mrow>  <mn> 2382000985 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <mroot>  <mn> 2 </mn>  <mn> 4 </mn>  </mroot>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <msqrt>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  </msqrt>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 3 </mn>  <mo> / </mo>  <mn> 4 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 3369074688 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 8 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 15070593024 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 7 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 26986856448 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 24430484736 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 11527353648 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 2568094191 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 182768994 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 2915457 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <msqrt>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  </msqrt>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 4492099584 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 9 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 23931125760 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 8 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 52996079616 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 7 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 62716993536 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 42295632960 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 15909017496 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 2957601621 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 181294510 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 2848435 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 134044 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 134044 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 47 <sep /> 8 </cn>  </apply>  <cn type='rational'> 45 <sep /> 8 </cn>  </list>  <list>  <cn type='rational'> 13 <sep /> 4 </cn>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2382000985 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 4 </cn>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='rational'> 1 <sep /> 4 </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'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <cn type='rational'> 3 <sep /> 4 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 3369074688 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 8 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 15070593024 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 7 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 26986856448 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 24430484736 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 11527353648 </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'> 2568094191 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 182768994 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 2915457 </cn>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 4492099584 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 9 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 23931125760 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 8 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 52996079616 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 7 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 62716993536 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 42295632960 </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'> 15909017496 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 2957601621 </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'> 181294510 </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'> 2848435 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='integer'> -134044 </cn>  </apply>  </apply>  <cn type='integer'> 134044 </cn>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["47", "8"]]], ",", FractionBox["45", "8"], ",", FractionBox["13", "4"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["4", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List["134044", "+", RowBox[List["2915457", " ", "z"]], "+", RowBox[List["182768994", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2568094191", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["11527353648", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["24430484736", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["26986856448", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["15070593024", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["3369074688", " ", SuperscriptBox["z", "8"]]], "+", FractionBox[RowBox[List[RowBox[List["-", "134044"]], "-", RowBox[List["2848435", " ", "z"]], "-", RowBox[List["181294510", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2957601621", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["15909017496", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["42295632960", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["62716993536", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["52996079616", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["23931125760", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["4492099584", " ", SuperscriptBox["z", "9"]]]]], SqrtBox[RowBox[List["1", "-", "z"]]]]]], ")"]]]], RowBox[List["2382000985", " ", SuperscriptBox["z", "3"]]]]]]]] | 
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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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