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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(9/4), 7/2, 1, z] == (1/(90 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]])) (22 (68 - 392 z + 399 z^2) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 22 Sqrt[1 - z] (68 - 392 z + 399 z^2) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 11 (68 - 392 z + 399 z^2) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 11 (1 - z)^(1/4) (68 - 392 z + 399 z^2) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 11 Sqrt[1 - z] (68 - 392 z + 399 z^2) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - ((388 - 1716 z + 1463 z^2) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/(1 - z)^(1/4))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["9", "4"]]], ",", FractionBox["7", "2"], ",", "1", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["90", " ", SqrtBox["2"], " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]], RowBox[List["(", RowBox[List[RowBox[List["22", " ", RowBox[List["(", RowBox[List["68", "-", RowBox[List["392", " ", "z"]], "+", RowBox[List["399", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List["22", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["68", "-", RowBox[List["392", " ", "z"]], "+", RowBox[List["399", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List["11", " ", RowBox[List["(", RowBox[List["68", "-", RowBox[List["392", " ", "z"]], "+", RowBox[List["399", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List["11", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["68", "-", RowBox[List["392", " ", "z"]], "+", RowBox[List["399", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List["11", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["68", "-", RowBox[List["392", " ", "z"]], "+", RowBox[List["399", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["388", "-", RowBox[List["1716", " ", "z"]], "+", RowBox[List["1463", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( - 9 4 , 7 2 ; 1 ; 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["9", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["1", 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 90 2 π 1 - z + 1 ( 22 1 - z ( 399 z 2 - 392 z + 68 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + 22 ( 399 z 2 - 392 z + 68 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) - 11 1 - z ( 399 z 2 - 392 z + 68 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) - 11 1 - z 4 ( 399 z 2 - 392 z + 68 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) - 11 ( 399 z 2 - 392 z + 68 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) - ( 1463 z 2 - 1716 z + 388 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) 1 - z 4 ) HypergeometricPFQ -1 9 4 7 2 1 z 1 90 2 1 2 1 -1 z 1 2 1 1 2 -1 22 1 -1 z 1 2 399 z 2 -1 392 z 68 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 22 399 z 2 -1 392 z 68 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 11 1 -1 z 1 2 399 z 2 -1 392 z 68 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 11 1 -1 z 1 4 399 z 2 -1 392 z 68 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 11 399 z 2 -1 392 z 68 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 1463 z 2 -1 1716 z 388 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 4 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["9", "4"]]], ",", FractionBox["7", "2"], ",", "1", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["22", " ", RowBox[List["(", RowBox[List["68", "-", RowBox[List["392", " ", "z"]], "+", RowBox[List["399", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List["22", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["68", "-", RowBox[List["392", " ", "z"]], "+", RowBox[List["399", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List["11", " ", RowBox[List["(", RowBox[List["68", "-", RowBox[List["392", " ", "z"]], "+", RowBox[List["399", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List["11", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["68", "-", RowBox[List["392", " ", "z"]], "+", RowBox[List["399", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List["11", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["68", "-", RowBox[List["392", " ", "z"]], "+", RowBox[List["399", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["388", "-", RowBox[List["1716", " ", "z"]], "+", RowBox[List["1463", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]], RowBox[List["90", " ", SqrtBox["2"], " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]]]]

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

 2007-05-02