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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.alf3.01

 Input Form

 Hypergeometric2F1[9/4, 21/4, 5/2, z] == (1/(16575 Pi^(3/2) z^(3/2))) (4 ((2 (-462 + 4851 z + 2500 z^2 - 905 z^3 + 160 z^4) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^5 - (2 (-462 + 4851 z + 2500 z^2 - 905 z^3 + 160 z^4) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^5 - (1/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^4)) ((-462 + 231 Sqrt[z] + 4620 z + 1930 z^(3/2) + 570 z^2 - 785 z^(5/2) - 120 z^3 + 160 z^(7/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^5)) ((462 + 231 Sqrt[z] - 4620 z + 1930 z^(3/2) - 570 z^2 - 785 z^(5/2) + 120 z^3 + 160 z^(7/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["9", "4"], ",", FractionBox["21", "4"], ",", FractionBox["5", "2"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["16575", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "462"]], "+", RowBox[List["4851", " ", "z"]], "+", RowBox[List["2500", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["905", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["160", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "5"]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "462"]], "+", RowBox[List["4851", " ", "z"]], "+", RowBox[List["2500", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["905", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["160", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "5"]], "-", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "4"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "462"]], "+", RowBox[List["231", " ", SqrtBox["z"]]], "+", RowBox[List["4620", " ", "z"]], "+", RowBox[List["1930", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["570", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["785", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["120", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["160", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "5"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["462", "+", RowBox[List["231", " ", SqrtBox["z"]]], "-", RowBox[List["4620", " ", "z"]], "+", RowBox[List["1930", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["570", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["785", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["120", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["160", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 9 4 , 21 4 ; 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[FractionBox["9", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["21", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[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 16575 π 3 / 2 z 3 / 2 ( 4 ( 2 ( 160 z 4 - 905 z 3 + 2500 z 2 + 4851 z - 462 ) E ( 1 2 ( 1 - z ) ) ( z - 1 ) 5 - 2 ( 160 z 4 - 905 z 3 + 2500 z 2 + 4851 z - 462 ) E ( 1 2 ( z + 1 ) ) ( z - 1 ) 5 - ( 160 z 7 / 2 - 120 z 3 - 785 z 5 / 2 + 570 z 2 + 1930 z 3 / 2 + 4620 z + 231 z - 462 ) K ( 1 2 ( 1 - z ) ) ( z - 1 ) 5 ( z + 1 ) 4 + ( 160 z 7 / 2 + 120 z 3 - 785 z 5 / 2 - 570 z 2 + 1930 z 3 / 2 - 4620 z + 231 z + 462 ) K ( 1 2 ( z + 1 ) ) ( z - 1 ) 4 ( z + 1 ) 5 ) Γ ( 3 4 ) 2 ) HypergeometricPFQ 9 4 21 4 5 2 z 1 16575 3 2 z 3 2 -1 4 2 160 z 4 -1 905 z 3 2500 z 2 4851 z -462 EllipticE 1 2 1 -1 z 1 2 z -1 5 -1 -1 2 160 z 4 -1 905 z 3 2500 z 2 4851 z -462 EllipticE 1 2 z 1 2 1 z -1 5 -1 -1 160 z 7 2 -1 120 z 3 -1 785 z 5 2 570 z 2 1930 z 3 2 4620 z 231 z 1 2 -462 EllipticK 1 2 1 -1 z 1 2 z 1 2 -1 5 z 1 2 1 4 -1 160 z 7 2 120 z 3 -1 785 z 5 2 -1 570 z 2 1930 z 3 2 -1 4620 z 231 z 1 2 462 EllipticK 1 2 z 1 2 1 z 1 2 -1 4 z 1 2 1 5 -1 Gamma 3 4 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["9", "4"], ",", FractionBox["21", "4"], ",", FractionBox["5", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "462"]], "+", RowBox[List["4851", " ", "z"]], "+", RowBox[List["2500", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["905", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["160", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "5"]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "462"]], "+", RowBox[List["4851", " ", "z"]], "+", RowBox[List["2500", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["905", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["160", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "5"]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "462"]], "+", RowBox[List["231", " ", SqrtBox["z"]]], "+", RowBox[List["4620", " ", "z"]], "+", RowBox[List["1930", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["570", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["785", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["120", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["160", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "4"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["462", "+", RowBox[List["231", " ", SqrtBox["z"]]], "-", RowBox[List["4620", " ", "z"]], "+", RowBox[List["1930", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["570", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["785", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["120", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["160", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "5"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], RowBox[List["16575", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]]]]]

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

 2007-05-02