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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.25.0005.01

 Input Form

 Limit[Limit[Hypergeometric2F1[a, b, c, z/(a b)], a -> Infinity], b -> Infinity] == Hypergeometric0F1[c, z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["a", ",", "b", ",", "c", ",", FractionBox["z", RowBox[List["a", " ", "b"]]]]], "]"]], ",", RowBox[List["a", "\[Rule]", "\[Infinity]"]]]], "]"]], ",", RowBox[List["b", "\[Rule]", "\[Infinity]"]]]], "]"]], "\[Equal]", RowBox[List["Hypergeometric0F1", "[", RowBox[List["c", ",", "z"]], "]"]]]]]]

 MathML Form

 lim b "\[Rule]" lim a "\[Rule]" 2 F 1 ( a , b ; c ; z a b ) 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["b", 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[FractionBox["z", RowBox[List["a", " ", "b"]]], Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] 0 F 1 ( ; c ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["0", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox["c", Hypergeometric0F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False]], ";", TagBox["z", Hypergeometric0F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric0F1] b b a a Hypergeometric2F1 a b c z a b -1 Hypergeometric0F1 c z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["a_", ",", "b_", ",", "c_", ",", FractionBox["z_", RowBox[List["a_", " ", "b_"]]]]], "]"]], ",", RowBox[List["a_", "\[Rule]", "\[Infinity]"]]]], "]"]], ",", RowBox[List["b_", "\[Rule]", "\[Infinity]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Hypergeometric0F1", "[", RowBox[List["c", ",", "z"]], "]"]]]]]]

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

 2001-10-29