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 | | http://functions.wolfram.com/07.23.03.c9wr.01 | 
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 | | Hypergeometric2F1[25/8, 45/8, -(35/8), z] == 
 -((1/(428127 (1 - z)^(105/8))) (-428127 + 7339320 z - 63607440 z^2 + 
    392803840 z^3 - 2249694720 z^4 + 25196580864 z^5 + 83988602880 z^6 + 
    44301680640 z^7 + 3164405760 z^8 - 96993280 z^9 + 3145728 z^10)) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["25", "8"], ",", FractionBox["45", "8"], ",", RowBox[List["-", FractionBox["35", "8"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List["428127", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["105", "/", "8"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["-", "428127"]], "+", RowBox[List["7339320", " ", "z"]], "-", RowBox[List["63607440", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["392803840", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["2249694720", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["25196580864", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["83988602880", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["44301680640", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["3164405760", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["96993280", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["3145728", " ", SuperscriptBox["z", "10"]]]]], ")"]]]]]]]]]] | 
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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>  <mfrac>  <mn> 25 </mn>  <mn> 8 </mn>  </mfrac>  <mo> , </mo>  <mfrac>  <mn> 45 </mn>  <mn> 8 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 35 </mn>  <mn> 8 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["25", "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[RowBox[List["-", FractionBox["35", "8"]]], 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>  <mo> - </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mrow>  <mn> 428127 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 105 </mn>  <mo> / </mo>  <mn> 8 </mn>  </mrow>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 3145728 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 10 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 96993280 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 9 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 3164405760 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 8 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 44301680640 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 7 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 83988602880 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 25196580864 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 2249694720 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 392803840 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 63607440 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 7339320 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 428127 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <cn type='rational'> 25 <sep /> 8 </cn>  <cn type='rational'> 45 <sep /> 8 </cn>  </list>  <list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 35 <sep /> 8 </cn>  </apply>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 428127 </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'> 105 <sep /> 8 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 3145728 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 10 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 96993280 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 9 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 3164405760 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 8 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 44301680640 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 7 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 83988602880 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 25196580864 </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'> 2249694720 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 392803840 </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'> 63607440 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 7339320 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> -428127 </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[FractionBox["25", "8"], ",", FractionBox["45", "8"], ",", RowBox[List["-", FractionBox["35", "8"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["-", "428127"]], "+", RowBox[List["7339320", " ", "z"]], "-", RowBox[List["63607440", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["392803840", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["2249694720", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["25196580864", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["83988602880", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["44301680640", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["3164405760", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["96993280", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["3145728", " ", SuperscriptBox["z", "10"]]]]], RowBox[List["428127", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["105", "/", "8"]]]]]]]]]]]] | 
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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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