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; }

 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.ajdw.01

 Input Form

 HypergeometricPFQ[{-(1/2), 1/2, 3/2}, {-(7/2), 2}, -z] == (4 (315 + 857 z + 742 z^2 + 192 z^3) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(105 Pi z (1 + z)^3) + (4 (315 + 857 z + 742 z^2 + 192 z^3) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(105 Pi z (1 + z)^(5/2)) - (16 (105 + 203 z + 96 z^2) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(105 Pi z (1 + z)^2) - (8 (105 + 241 z + 144 z^2) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(105 Pi z (1 + z)^(5/2))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", FractionBox["1", "2"], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", "2"]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List["315", "+", RowBox[List["857", " ", "z"]], "+", RowBox[List["742", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["192", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"]], "]"]]]], RowBox[List["105", " ", "\[Pi]", " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "3"]]]], "+", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List["315", "+", RowBox[List["857", " ", "z"]], "+", RowBox[List["742", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["192", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"]], "]"]]]], RowBox[List["105", " ", "\[Pi]", " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["16", " ", RowBox[List["(", RowBox[List["105", "+", RowBox[List["203", " ", "z"]], "+", RowBox[List["96", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"]], "]"]]]], RowBox[List["105", " ", "\[Pi]", " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "2"]]]], "-", FractionBox[RowBox[List["8", " ", RowBox[List["(", RowBox[List["105", "+", RowBox[List["241", " ", "z"]], "+", RowBox[List["144", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"]], "]"]]]], RowBox[List["105", " ", "\[Pi]", " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]]]]]]]]

 MathML Form

 3 F 2 ( - 1 2 , 1 2 , 3 2 ; - 7 2 , 2 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["7", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "z"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] 4 ( 192 z 3 + 742 z 2 + 857 z + 315 ) E ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 105 π z ( z + 1 ) 5 / 2 + 4 ( 192 z 3 + 742 z 2 + 857 z + 315 ) E ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 105 π z ( z + 1 ) 3 - 16 ( 96 z 2 + 203 z + 105 ) K ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 105 π z ( z + 1 ) 2 - 8 ( 144 z 2 + 241 z + 105 ) K ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 105 π z ( z + 1 ) 5 / 2 HypergeometricPFQ -1 1 2 1 2 3 2 -1 7 2 2 -1 z 4 192 z 3 742 z 2 857 z 315 EllipticE z 1 1 2 -1 2 z 1 1 2 1 2 -1 105 z z 1 5 2 -1 4 192 z 3 742 z 2 857 z 315 EllipticE z 1 1 2 -1 2 z 1 1 2 1 2 -1 105 z z 1 3 -1 -1 16 96 z 2 203 z 105 EllipticK z 1 1 2 -1 2 z 1 1 2 1 2 -1 105 z z 1 2 -1 -1 8 144 z 2 241 z 105 EllipticK z 1 1 2 -1 2 z 1 1 2 1 2 -1 105 z z 1 5 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", FractionBox["1", "2"], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", "2"]], "}"]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List["315", "+", RowBox[List["857", " ", "z"]], "+", RowBox[List["742", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["192", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"]], "]"]]]], RowBox[List["105", " ", "\[Pi]", " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "3"]]]], "+", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List["315", "+", RowBox[List["857", " ", "z"]], "+", RowBox[List["742", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["192", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"]], "]"]]]], RowBox[List["105", " ", "\[Pi]", " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["16", " ", RowBox[List["(", RowBox[List["105", "+", RowBox[List["203", " ", "z"]], "+", RowBox[List["96", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"]], "]"]]]], RowBox[List["105", " ", "\[Pi]", " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "2"]]]], "-", FractionBox[RowBox[List["8", " ", RowBox[List["(", RowBox[List["105", "+", RowBox[List["241", " ", "z"]], "+", RowBox[List["144", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]], "2"]], "]"]]]], RowBox[List["105", " ", "\[Pi]", " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]]]]]]]]

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

 2007-05-02