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 | | http://functions.wolfram.com/07.23.03.abhs.01 | 
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 | | Hypergeometric2F1[-(15/4), 2, 21/4, z] == (1/(469762048 z^(17/4))) 
  (221 (2 z^(1/4) (45045 - 240471 z + 440209 z^2 - 121275 z^3 + 333711 z^4 - 
      302325 z^5 + 129195 z^6 - 21945 z^7) + 3465 (-1 + z)^7 (13 + 19 z) 
     ArcTan[z^(1/4)] + 3465 (-1 + z)^7 (13 + 19 z) ArcTanh[z^(1/4)])) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["15", "4"]]], ",", "2", ",", FractionBox["21", "4"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["469762048", " ", SuperscriptBox["z", RowBox[List["17", "/", "4"]]]]]], RowBox[List["(", RowBox[List["221", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["45045", "-", RowBox[List["240471", " ", "z"]], "+", RowBox[List["440209", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["121275", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["333711", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["302325", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["129195", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["21945", " ", SuperscriptBox["z", "7"]]]]], ")"]]]], "+", RowBox[List["3465", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"], " ", RowBox[List["(", RowBox[List["13", "+", RowBox[List["19", " ", "z"]]]], ")"]], " ", RowBox[List["ArcTan", "[", SuperscriptBox["z", RowBox[List["1", "/", "4"]]], "]"]]]], "+", RowBox[List["3465", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"], " ", RowBox[List["(", RowBox[List["13", "+", RowBox[List["19", " ", "z"]]]], ")"]], " ", RowBox[List["ArcTanh", "[", SuperscriptBox["z", RowBox[List["1", "/", "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> 15 </mn>  <mn> 4 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mn> 2 </mn>  </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["15", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["2", 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>  <mfrac>  <mn> 1 </mn>  <mrow>  <mn> 469762048 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 17 </mn>  <mo> / </mo>  <mn> 4 </mn>  </mrow>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 221 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 3465 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 19 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 13 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msup>  <mi> tan </mi>  <mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </msup>  <mo> ( </mo>  <mroot>  <mi> z </mi>  <mn> 4 </mn>  </mroot>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 7 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 3465 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 19 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 13 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msup>  <mi> tanh </mi>  <mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </msup>  <mo> ( </mo>  <mroot>  <mi> z </mi>  <mn> 4 </mn>  </mroot>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 7 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mroot>  <mi> z </mi>  <mn> 4 </mn>  </mroot>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mn> 21945 </mn>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 7 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 129195 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 302325 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 333711 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 121275 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 440209 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 240471 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 45045 </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'> 15 <sep /> 4 </cn>  </apply>  <cn type='integer'> 2 </cn>  </list>  <list>  <cn type='rational'> 21 <sep /> 4 </cn>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 469762048 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 17 <sep /> 4 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 221 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 3465 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 19 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 13 </cn>  </apply>  <apply>  <arctan />  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 4 </cn>  </apply>  </apply>  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> -1 </cn>  </apply>  <cn type='integer'> 7 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 3465 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 19 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 13 </cn>  </apply>  <apply>  <arctanh />  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 4 </cn>  </apply>  </apply>  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> -1 </cn>  </apply>  <cn type='integer'> 7 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 4 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -21945 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 7 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 129195 </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'> 302325 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 333711 </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'> 121275 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 440209 </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'> 240471 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='integer'> 45045 </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["15", "4"]]], ",", "2", ",", FractionBox["21", "4"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["221", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["45045", "-", RowBox[List["240471", " ", "z"]], "+", RowBox[List["440209", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["121275", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["333711", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["302325", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["129195", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["21945", " ", SuperscriptBox["z", "7"]]]]], ")"]]]], "+", RowBox[List["3465", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"], " ", RowBox[List["(", RowBox[List["13", "+", RowBox[List["19", " ", "z"]]]], ")"]], " ", RowBox[List["ArcTan", "[", SuperscriptBox["z", RowBox[List["1", "/", "4"]]], "]"]]]], "+", RowBox[List["3465", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"], " ", RowBox[List["(", RowBox[List["13", "+", RowBox[List["19", " ", "z"]]]], ")"]], " ", RowBox[List["ArcTanh", "[", SuperscriptBox["z", RowBox[List["1", "/", "4"]]], "]"]]]]]], ")"]]]], RowBox[List["469762048", " ", SuperscriptBox["z", RowBox[List["17", "/", "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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