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 | | http://functions.wolfram.com/07.23.03.aaoa.01 | 
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 | | Hypergeometric2F1[-(17/4), 9/4, 11/2, z] == (1/(2235255 z^(9/2))) 
  (16 ((1 + Sqrt[z])^(15/2) (3536 - 26520 Sqrt[z] + 92820 z - 
      207740 z^(3/2) + 341445 z^2 - 436254 z^(5/2) + 433160 z^3 - 
      318240 z^(7/2) + 159120 z^4 - 47520 z^(9/2) + 6336 z^5) - 
    (1 - Sqrt[z])^(15/2) (3536 + 26520 Sqrt[z] + 92820 z + 207740 z^(3/2) + 
      341445 z^2 + 436254 z^(5/2) + 433160 z^3 + 318240 z^(7/2) + 
      159120 z^4 + 47520 z^(9/2) + 6336 z^5))) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["17", "4"]]], ",", FractionBox["9", "4"], ",", FractionBox["11", "2"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2235255", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]], RowBox[List["(", RowBox[List["16", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], RowBox[List["15", "/", "2"]]], " ", RowBox[List["(", RowBox[List["3536", "-", RowBox[List["26520", " ", SqrtBox["z"]]], "+", RowBox[List["92820", " ", "z"]], "-", RowBox[List["207740", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["341445", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["436254", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["433160", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["318240", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["159120", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["47520", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["6336", " ", SuperscriptBox["z", "5"]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]], RowBox[List["15", "/", "2"]]], " ", RowBox[List["(", RowBox[List["3536", "+", RowBox[List["26520", " ", SqrtBox["z"]]], "+", RowBox[List["92820", " ", "z"]], "+", RowBox[List["207740", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["341445", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["436254", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["433160", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["318240", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["159120", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["47520", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["6336", " ", SuperscriptBox["z", "5"]]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]] | 
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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> 17 </mn>  <mn> 4 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mfrac>  <mn> 9 </mn>  <mn> 4 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mfrac>  <mn> 11 </mn>  <mn> 2 </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["17", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["11", "2"], 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> 2235255 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 9 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 16 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 15 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 6336 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 47520 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 9 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 159120 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 318240 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 7 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 433160 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 436254 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 5 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 341445 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 207740 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 3 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 92820 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mrow>  <mn> 26520 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  <mo> + </mo>  <mn> 3536 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 15 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 6336 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 47520 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 9 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 159120 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 318240 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 7 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 433160 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 436254 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 5 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 341445 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 207740 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 3 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 92820 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mrow>  <mn> 26520 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> z </mi>  </msqrt>  </mrow>  <mo> + </mo>  <mn> 3536 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </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'> 17 <sep /> 4 </cn>  </apply>  <cn type='rational'> 9 <sep /> 4 </cn>  </list>  <list>  <cn type='rational'> 11 <sep /> 2 </cn>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2235255 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 9 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 16 </cn>  <apply>  <plus />  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <cn type='rational'> 15 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 6336 </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'> 47520 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 9 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 159120 </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'> 318240 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 7 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 433160 </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'> 436254 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 5 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 341445 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 207740 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 3 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 92820 </cn>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 26520 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <cn type='integer'> 3536 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <cn type='rational'> 15 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 6336 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 47520 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 9 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 159120 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 318240 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 7 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 433160 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 436254 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 5 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 341445 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 207740 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 3 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 92820 </cn>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> 26520 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> 3536 </cn>  </apply>  </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["17", "4"]]], ",", FractionBox["9", "4"], ",", FractionBox["11", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["16", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], RowBox[List["15", "/", "2"]]], " ", RowBox[List["(", RowBox[List["3536", "-", RowBox[List["26520", " ", SqrtBox["z"]]], "+", RowBox[List["92820", " ", "z"]], "-", RowBox[List["207740", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["341445", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["436254", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["433160", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["318240", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["159120", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["47520", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["6336", " ", SuperscriptBox["z", "5"]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]], RowBox[List["15", "/", "2"]]], " ", RowBox[List["(", RowBox[List["3536", "+", RowBox[List["26520", " ", SqrtBox["z"]]], "+", RowBox[List["92820", " ", "z"]], "+", RowBox[List["207740", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["341445", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["436254", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["433160", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["318240", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["159120", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["47520", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["6336", " ", SuperscriptBox["z", "5"]]]]], ")"]]]]]], ")"]]]], RowBox[List["2235255", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]]]]] | 
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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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