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 | | http://functions.wolfram.com/07.23.03.a9u2.01 | 
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 | | Hypergeometric2F1[-(19/4), 5, 15/4, z] == (1/(245366784 z^(11/4))) 
  (4 z^(3/4) (10241 + 100947 z + 62754669 z^2 - 431534137 z^3 + 
     1115793411 z^4 - 1385497575 z^5 + 835538319 z^6 - 197149491 z^7) - 
   4389 (1 - z)^(7/2) (7 + 92 z + 1242 z^2 - 25668 z^3 + 44919 z^4) 
    Beta[z, 3/4, 1/2]) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["19", "4"]]], ",", "5", ",", FractionBox["15", "4"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["245366784", " ", SuperscriptBox["z", RowBox[List["11", "/", "4"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List["10241", "+", RowBox[List["100947", " ", "z"]], "+", RowBox[List["62754669", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["431534137", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1115793411", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1385497575", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["835538319", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["197149491", " ", SuperscriptBox["z", "7"]]]]], ")"]]]], "-", RowBox[List["4389", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["7", "/", "2"]]], " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["92", " ", "z"]], "+", RowBox[List["1242", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["25668", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["44919", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Beta", "[", RowBox[List["z", ",", FractionBox["3", "4"], ",", FractionBox["1", "2"]]], "]"]]]]]], ")"]]]]]]]] | 
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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> 19 </mn>  <mn> 4 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mn> 5 </mn>  </mrow>  <mo> ; </mo>  <mfrac>  <mn> 15 </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["19", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["15", "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> 245366784 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 11 </mn>  <mo> / </mo>  <mn> 4 </mn>  </mrow>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 3 </mn>  <mo> / </mo>  <mn> 4 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mn> 197149491 </mn>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 7 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 835538319 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 1385497575 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 1115793411 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 431534137 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 62754669 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 100947 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 10241 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mrow>  <mn> 4389 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 7 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 44919 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 25668 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 1242 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 92 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 7 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msub>  <semantics>  <mi> Β </mi>  <annotation-xml encoding='MathML-Content'>  <ci> Beta </ci>  </annotation-xml>  </semantics>  <mi> z </mi>  </msub>  <mo> ( </mo>  <mrow>  <mfrac>  <mn> 3 </mn>  <mn> 4 </mn>  </mfrac>  <mo> , </mo>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  </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'> 19 <sep /> 4 </cn>  </apply>  <cn type='integer'> 5 </cn>  </list>  <list>  <cn type='rational'> 15 <sep /> 4 </cn>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 245366784 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 11 <sep /> 4 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 4 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 3 <sep /> 4 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -197149491 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 7 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 835538319 </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'> 1385497575 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 1115793411 </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'> 431534137 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 62754669 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 100947 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 10241 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 4389 </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'> 7 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 44919 </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'> 25668 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 1242 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 92 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 7 </cn>  </apply>  <apply>  <ci> Beta </ci>  <ci> z </ci>  <cn type='rational'> 3 <sep /> 4 </cn>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </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["19", "4"]]], ",", "5", ",", FractionBox["15", "4"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List["10241", "+", RowBox[List["100947", " ", "z"]], "+", RowBox[List["62754669", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["431534137", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1115793411", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1385497575", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["835538319", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["197149491", " ", SuperscriptBox["z", "7"]]]]], ")"]]]], "-", RowBox[List["4389", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["7", "/", "2"]]], " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["92", " ", "z"]], "+", RowBox[List["1242", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["25668", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["44919", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Beta", "[", RowBox[List["z", ",", FractionBox["3", "4"], ",", FractionBox["1", "2"]]], "]"]]]]]], RowBox[List["245366784", " ", SuperscriptBox["z", RowBox[List["11", "/", "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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