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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.0633.01

 Input Form

 Hypergeometric2F1[-2 n, n + 1/2, n + 1, 4/3] == 3^(-2 n) /; Element[n, Integers] && n >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List[RowBox[List["-", "2"]], "n"]], ",", RowBox[List["n", "+", FractionBox["1", "2"]]], ",", RowBox[List["n", "+", "1"]], ",", FractionBox["4", "3"]]], "]"]], "\[Equal]", SuperscriptBox["3", RowBox[List[RowBox[List["-", "2"]], "n"]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 2 F 1 ( a , 2 a - 1 2 ; 4 a - 1 ; 12 2 - 16 ) 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[RowBox[List["2", " ", "a"]], "-", FractionBox["1", "2"]]], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List[RowBox[List["4", " ", "a"]], "-", "1"]], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[RowBox[List[RowBox[List["12", " ", SqrtBox["2"]]], "-", "16"]], Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] ( 2 + 2 ) 2 a π Γ ( 2 a ) 2 4 a - 1 Γ ( a + 1 2 ) Γ ( 3 a 2 ) /; n Condition Hypergeometric2F1 a 2 a -1 1 2 4 a -1 12 2 1 2 -16 2 2 1 2 2 a 1 2 Gamma 2 a 2 4 a -1 Gamma a 1 2 -1 Gamma 3 a 2 -1 -1 n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "n_"]], ",", RowBox[List["n_", "+", FractionBox["1", "2"]]], ",", RowBox[List["n_", "+", "1"]], ",", FractionBox["4", "3"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["3", RowBox[List[RowBox[List["-", "2"]], " ", "n"]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2001-10-29