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 | | http://functions.wolfram.com/07.23.03.1854.01 | 
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 | | Hypergeometric2F1[-(7/2), 5, 7/2, z] == (1/(131072 z^(5/2))) 
  ((-Sqrt[z]) (105 + 
     z (1085 + 3 z (-37442 + 385 z (382 + 13 z (-37 + 15 z))))) + 
   105 (-1 + z)^2 (1 + 3 z (4 + 11 z (6 + 13 z (-4 + 5 z)))) ArcTanh[Sqrt[z]]) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", "5", ",", FractionBox["7", "2"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["131072", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SqrtBox["z"]]], " ", RowBox[List["(", RowBox[List["105", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1085", "+", RowBox[List["3", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "37442"]], "+", RowBox[List["385", " ", "z", " ", RowBox[List["(", RowBox[List["382", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "37"]], "+", RowBox[List["15", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["105", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["3", " ", "z", " ", RowBox[List["(", RowBox[List["4", "+", RowBox[List["11", " ", "z", " ", RowBox[List["(", RowBox[List["6", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["5", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcTanh", "[", SqrtBox["z"], "]"]]]]]], ")"]]]]]]]] | 
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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> 7 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mn> 5 </mn>  </mrow>  <mo> ; </mo>  <mfrac>  <mn> 7 </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["7", "2"]]], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["5", Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["7", "2"], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], Hypergeometric2F1] </annotation>  </semantics>  <mo>  </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mrow>  <mn> 131072 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 5 </mn>  <mo> / </mo>  <mn> 2 </mn>  </mrow>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 105 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 3 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 11 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 13 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 5 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 4 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 6 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 4 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msup>  <mi> tanh </mi>  <mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> - </mo>  <mrow>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 3 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 385 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 13 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 15 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 37 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 382 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mn> 37442 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 1085 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 105 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> Hypergeometric2F1 </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 7 <sep /> 2 </cn>  </apply>  <cn type='integer'> 5 </cn>  <cn type='rational'> 7 <sep /> 2 </cn>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 131072 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 5 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 105 </cn>  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> -1 </cn>  </apply>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 3 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 11 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 13 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 5 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> -4 </cn>  </apply>  </apply>  <cn type='integer'> 6 </cn>  </apply>  </apply>  <cn type='integer'> 4 </cn>  </apply>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <times />  <apply>  <power />  <ci> tanh </ci>  <cn type='integer'> -1 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 3 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 385 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 13 </cn>  <ci> z </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 15 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> -37 </cn>  </apply>  </apply>  <cn type='integer'> 382 </cn>  </apply>  </apply>  <cn type='integer'> -37442 </cn>  </apply>  </apply>  <cn type='integer'> 1085 </cn>  </apply>  </apply>  <cn type='integer'> 105 </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["7", "2"]]], ",", "5", ",", FractionBox["7", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", SqrtBox["z"]]], " ", RowBox[List["(", RowBox[List["105", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1085", "+", RowBox[List["3", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "37442"]], "+", RowBox[List["385", " ", "z", " ", RowBox[List["(", RowBox[List["382", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "37"]], "+", RowBox[List["15", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["105", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["3", " ", "z", " ", RowBox[List["(", RowBox[List["4", "+", RowBox[List["11", " ", "z", " ", RowBox[List["(", RowBox[List["6", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["5", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcTanh", "[", SqrtBox["z"], "]"]]]]]], RowBox[List["131072", " ", SuperscriptBox["z", RowBox[List["5", "/", "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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