html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[31/8, 37/8, 2, z] == (1/(303485 Pi (-1 + z)^7 z)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-1 + z) (455 + 15767 z + 16765 z^2 + 805 z^3) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 20 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (1911 + 5074 z + 1463 z^2) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-37765 - 85713 z - 12495 z^2 + 805 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-1 + z) (455 + 15767 z + 16765 z^2 + 805 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["31", "8"], ",", FractionBox["37", "8"], ",", "2", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["303485", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"], " ", "z"]]], RowBox[List["(", RowBox[List["8", " ", SuperscriptBox["2", RowBox[List["3", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["455", "+", RowBox[List["15767", " ", "z"]], "+", RowBox[List["16765", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["805", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List["20", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["1911", "+", RowBox[List["5074", " ", "z"]], "+", RowBox[List["1463", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "37765"]], "-", RowBox[List["85713", " ", "z"]], "-", RowBox[List["12495", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["805", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["455", "+", RowBox[List["15767", " ", "z"]], "+", RowBox[List["16765", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["805", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 31 8 , 37 8 ; 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["31", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["37", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["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 303485 π ( z - 1 ) 7 z ( 8 2 3 / 4 1 - z + 1 4 ( 4 ( z - 1 ) ( 805 z 3 + 16765 z 2 + 15767 z + 455 ) E ( 1 2 - 1 2 1 - z + 1 ) - 20 2 1 - z + 1 ( z - 1 ) ( 1463 z 2 + 5074 z + 1911 ) K ( 1 2 - 1 2 1 - z + 1 ) + 2 1 - z + 1 1 - z ( 805 z 3 - 12495 z 2 - 85713 z - 37765 ) K ( 1 2 - 1 2 1 - z + 1 ) - 2 ( z - 1 ) ( 805 z 3 + 16765 z 2 + 15767 z + 455 ) K ( 1 2 - 1 2 1 - z + 1 ) ) ) HypergeometricPFQ 31 8 37 8 2 z 1 303485 z -1 7 z -1 8 2 3 4 1 -1 z 1 2 1 1 4 4 z -1 805 z 3 16765 z 2 15767 z 455 EllipticE 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 20 2 1 2 1 -1 z 1 2 1 1 2 z -1 1463 z 2 5074 z 1911 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 2 805 z 3 -1 12495 z 2 -1 85713 z -37765 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 2 z -1 805 z 3 16765 z 2 15767 z 455 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["31", "8"], ",", FractionBox["37", "8"], ",", "2", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["8", " ", SuperscriptBox["2", RowBox[List["3", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["455", "+", RowBox[List["15767", " ", "z"]], "+", RowBox[List["16765", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["805", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List["20", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["1911", "+", RowBox[List["5074", " ", "z"]], "+", RowBox[List["1463", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "37765"]], "-", RowBox[List["85713", " ", "z"]], "-", RowBox[List["12495", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["805", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["455", "+", RowBox[List["15767", " ", "z"]], "+", RowBox[List["16765", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["805", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["303485", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"], " ", "z"]]]]]]]

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

 2007-05-02