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 | | http://functions.wolfram.com/07.23.03.0113.01 | 
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 | | Hypergeometric2F1[a, 1 - a, c, z] == ((z - 1)^((c - 1)/2)/z^((c - 1)/2)) 
  Gamma[c] LegendreP[-a, 1 - c, 3, 1 - 2 z] | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["a", ",", RowBox[List["1", "-", "a"]], ",", "c", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], FractionBox[RowBox[List["c", "-", "1"]], "2"]], SuperscriptBox["z", FractionBox[RowBox[List["c", "-", "1"]], "2"]]], RowBox[List["Gamma", "[", "c", "]"]], RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["-", "a"]], ",", RowBox[List["1", "-", "c"]], ",", "3", ",", RowBox[List["1", "-", RowBox[List["2", "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>  <mi> a </mi>  <mo> , </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> a </mi>  </mrow>  </mrow>  <mo> ; </mo>  <mi> c </mi>  <mo> ; </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["a", Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "a"]], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox["c", Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox["z", Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] </annotation>  </semantics>  <mo> ⩵ </mo>  <mrow>  <mfrac>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mfrac>  <mrow>  <mi> c </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mn> 2 </mn>  </mfrac>  </msup>  <msup>  <mi> z </mi>  <mfrac>  <mrow>  <mi> c </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mn> 2 </mn>  </mfrac>  </msup>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> c </mi>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mstyle scriptlevel='0'>  <msubsup>  <semantics>  <mi> 𝔓 </mi>  <annotation encoding='Mathematica'> TagBox["\[GothicCapitalP]", LegendreQ] </annotation>  </semantics>  <mrow>  <mo> - </mo>  <mi> a </mi>  </mrow>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> c </mi>  </mrow>  </msubsup>  </mstyle>  <mo> ( </mo>  <mstyle scriptlevel='0'>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mrow>  </mstyle>  <mstyle scriptlevel='0'>  <mo> ) </mo>  </mstyle>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> Hypergeometric2F1 </ci>  <ci> a </ci>  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> a </ci>  </apply>  </apply>  <ci> c </ci>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> -1 </cn>  </apply>  <apply>  <times />  <apply>  <plus />  <ci> c </ci>  <cn type='integer'> -1 </cn>  </apply>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <power />  <apply>  <power />  <ci> z </ci>  <apply>  <times />  <apply>  <plus />  <ci> c </ci>  <cn type='integer'> -1 </cn>  </apply>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <ci> Gamma </ci>  <ci> c </ci>  </apply>  <apply>  <apply>  <power />  <apply>  <ci> Subscript </ci>  <apply>  <ci> LegendreQ </ci>  <ci> 𝔓 </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> a </ci>  </apply>  </apply>  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  </apply>  </apply>  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> z </ci>  </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["a_", ",", RowBox[List["1", "-", "a_"]], ",", "c_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], FractionBox[RowBox[List["c", "-", "1"]], "2"]], " ", RowBox[List["Gamma", "[", "c", "]"]], " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["-", "a"]], ",", RowBox[List["1", "-", "c"]], ",", "3", ",", RowBox[List["1", "-", RowBox[List["2", " ", "z"]]]]]], "]"]]]], SuperscriptBox["z", FractionBox[RowBox[List["c", "-", "1"]], "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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