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 | | http://functions.wolfram.com/07.24.17.0127.01 | 
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 | | Hypergeometric2F1Regularized[a, 3 a - 3/2, 3/2, z] == 
  (1 - z/9) (1 + z/3)^(1/2 - 3 a) Hypergeometric2F1Regularized[a - 1/6, 
    a + 1/6, 3/2, (z (z - 9)^2)/(z + 3)^3] /; Abs[z] < 1 | 
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 | | Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["a", ",", RowBox[List[RowBox[List["3", "a"]], "-", FractionBox["3", "2"]]], ",", FractionBox["3", "2"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List["1", "-", FractionBox["z", "9"]]], ")"]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox["z", "3"]]], ")"]], RowBox[List[FractionBox["1", "2"], "-", RowBox[List["3", "a"]]]]], " ", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List[RowBox[List["a", "-", FractionBox["1", "6"]]], ",", RowBox[List["a", "+", FractionBox["1", "6"]]], ",", FractionBox["3", "2"], ",", FractionBox[RowBox[List["z", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "9"]], ")"]], "2"]]], SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "3"]], ")"]], "3"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]] | 
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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>  <mrow>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 2 </mn>  </msub>  <msub>  <mover>  <mi> F </mi>  <mo> ~ </mo>  </mover>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> a </mi>  <mo> , </mo>  <mrow>  <mrow>  <mn> 3 </mn>  <mo> ⁢ </mo>  <mi> a </mi>  </mrow>  <mo> - </mo>  <mfrac>  <mn> 3 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  </mrow>  <mo> ; </mo>  <mfrac>  <mn> 3 </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]", FormBox["2", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["a", Hypergeometric2F1Regularized, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["3", " ", "a"]], "-", FractionBox["3", "2"]]], Hypergeometric2F1Regularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[FractionBox["3", "2"], Hypergeometric2F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox["z", Hypergeometric2F1Regularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1Regularized] </annotation>  </semantics>  <mo> ⩵ </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mfrac>  <mi> z </mi>  <mn> 9 </mn>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mfrac>  <mi> z </mi>  <mn> 3 </mn>  </mfrac>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  <mo> - </mo>  <mrow>  <mn> 3 </mn>  <mo> ⁢ </mo>  <mi> a </mi>  </mrow>  </mrow>  </msup>  <mo> ⁢ </mo>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 2 </mn>  </msub>  <msub>  <mover>  <mi> F </mi>  <mo> ~ </mo>  </mover>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mi> a </mi>  <mo> - </mo>  <mfrac>  <mn> 1 </mn>  <mn> 6 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mfrac>  <mn> 1 </mn>  <mn> 6 </mn>  </mfrac>  </mrow>  </mrow>  <mo> ; </mo>  <mfrac>  <mn> 3 </mn>  <mn> 2 </mn>  </mfrac>  <mo> ; </mo>  <mfrac>  <mrow>  <mi> z </mi>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> - </mo>  <mn> 9 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  </mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> + </mo>  <mn> 3 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 3 </mn>  </msup>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["a", "-", FractionBox["1", "6"]]], Hypergeometric2F1Regularized, Rule[Editable, True]], ",", TagBox[RowBox[List["a", "+", FractionBox["1", "6"]]], Hypergeometric2F1Regularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[FractionBox["3", "2"], Hypergeometric2F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[FractionBox[RowBox[List["z", " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "9"]], ")"]], "2"]]], SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "3"]], ")"]], "3"]], Hypergeometric2F1Regularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1Regularized] </annotation>  </semantics>  </mrow>  </mrow>  <mo> /; 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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["a_", ",", RowBox[List[RowBox[List["3", " ", "a_"]], "-", FractionBox["3", "2"]]], ",", FractionBox["3", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", FractionBox["z", "9"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox["z", "3"]]], ")"]], RowBox[List[FractionBox["1", "2"], "-", RowBox[List["3", " ", "a"]]]]], " ", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List[RowBox[List["a", "-", FractionBox["1", "6"]]], ",", RowBox[List["a", "+", FractionBox["1", "6"]]], ",", FractionBox["3", "2"], ",", FractionBox[RowBox[List["z", " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "9"]], ")"]], "2"]]], SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "3"]], ")"]], "3"]]]], "]"]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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 | | HypergeometricPFQRegularized[{},{b},z] |  | HypergeometricPFQRegularized[{a1},{b1},z] |  | HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] |  |  | 
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