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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.bd9k.01

 Input Form

 Hypergeometric2F1[-(35/8), 41/8, -(5/2), z] == (1/10880) ((1/(1 + Sqrt[z])^(13/4)) (5440 + 17680 Sqrt[z] + 68680 z + 166855 z^(3/2) + 515100 z^2 + 1166880 z^(5/2) + 5026560 z^3 + 42961152 z^(7/2) + 90614784 z^4 - 3461120 z^(9/2) - 185729024 z^5 - 188284928 z^(11/2) - 57933824 z^6) + (1/(1 - Sqrt[z])^(13/4)) (5440 - 17680 Sqrt[z] + 68680 z - 166855 z^(3/2) + 515100 z^2 - 1166880 z^(5/2) + 5026560 z^3 - 42961152 z^(7/2) + 90614784 z^4 + 3461120 z^(9/2) - 185729024 z^5 + 188284928 z^(11/2) - 57933824 z^6))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["35", "8"]]], ",", FractionBox["41", "8"], ",", RowBox[List["-", FractionBox["5", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "10880"], RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], RowBox[List["13", "/", "4"]]]], RowBox[List["(", RowBox[List["5440", "+", RowBox[List["17680", " ", SqrtBox["z"]]], "+", RowBox[List["68680", " ", "z"]], "+", RowBox[List["166855", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["515100", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1166880", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["5026560", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["42961152", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["90614784", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["3461120", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "-", RowBox[List["185729024", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["188284928", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "-", RowBox[List["57933824", " ", SuperscriptBox["z", "6"]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]], RowBox[List["13", "/", "4"]]]], RowBox[List["(", RowBox[List["5440", "-", RowBox[List["17680", " ", SqrtBox["z"]]], "+", RowBox[List["68680", " ", "z"]], "-", RowBox[List["166855", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["515100", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1166880", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["5026560", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["42961152", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["90614784", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["3461120", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "-", RowBox[List["185729024", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["188284928", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "-", RowBox[List["57933824", " ", SuperscriptBox["z", "6"]]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( - 35 8 , 41 8 ; - 5 2 ; z ) 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["35", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["41", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["5", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] 1 10880 ( 1 ( z + 1 ) 13 / 4 ( - 57933824 z 6 - 188284928 z 11 / 2 - 185729024 z 5 - 3461120 z 9 / 2 + 90614784 z 4 + 42961152 z 7 / 2 + 5026560 z 3 + 1166880 z 5 / 2 + 515100 z 2 + 166855 z 3 / 2 + 68680 z + 17680 z + 5440 ) + 1 ( 1 - z ) 13 / 4 ( - 57933824 z 6 + 188284928 z 11 / 2 - 185729024 z 5 + 3461120 z 9 / 2 + 90614784 z 4 - 42961152 z 7 / 2 + 5026560 z 3 - 1166880 z 5 / 2 + 515100 z 2 - 166855 z 3 / 2 + 68680 z - 17680 z + 5440 ) ) HypergeometricPFQ -1 35 8 41 8 -1 5 2 z 1 10880 1 z 1 2 1 13 4 -1 -57933824 z 6 -1 188284928 z 11 2 -1 185729024 z 5 -1 3461120 z 9 2 90614784 z 4 42961152 z 7 2 5026560 z 3 1166880 z 5 2 515100 z 2 166855 z 3 2 68680 z 17680 z 1 2 5440 1 1 -1 z 1 2 13 4 -1 -57933824 z 6 188284928 z 11 2 -1 185729024 z 5 3461120 z 9 2 90614784 z 4 -1 42961152 z 7 2 5026560 z 3 -1 1166880 z 5 2 515100 z 2 -1 166855 z 3 2 68680 z -1 17680 z 1 2 5440 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["35", "8"]]], ",", FractionBox["41", "8"], ",", RowBox[List["-", FractionBox["5", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[FractionBox[RowBox[List["5440", "+", RowBox[List["17680", " ", SqrtBox["z"]]], "+", RowBox[List["68680", " ", "z"]], "+", RowBox[List["166855", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["515100", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1166880", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["5026560", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["42961152", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["90614784", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["3461120", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "-", RowBox[List["185729024", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["188284928", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "-", RowBox[List["57933824", " ", SuperscriptBox["z", "6"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], RowBox[List["13", "/", "4"]]]], "+", FractionBox[RowBox[List["5440", "-", RowBox[List["17680", " ", SqrtBox["z"]]], "+", RowBox[List["68680", " ", "z"]], "-", RowBox[List["166855", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["515100", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1166880", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["5026560", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["42961152", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["90614784", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["3461120", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "-", RowBox[List["185729024", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["188284928", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "-", RowBox[List["57933824", " ", SuperscriptBox["z", "6"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]], RowBox[List["13", "/", "4"]]]]]], "10880"]]]]]

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

 2007-05-02