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.av7s.01

 Input Form

 HypergeometricPFQ[{7/2, 7/2, 7/2}, {3/2, 4}, -z] == -((32 (24 + 113 z + 212 z^2 + 13 z^3 + 274 z^4) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (1125 Pi z^3 (1 + z)^5)) - (32 (24 + 113 z + 212 z^2 + 13 z^3 + 274 z^4) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (1125 Pi z^3 (1 + z)^(9/2)) + (128 (6 + 23 z - 2 z^2 + 77 z^3) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (1125 Pi z^3 (1 + z)^4) + (64 (12 + 55 z + 170 z^2 - 137 z^3 + 120 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (1125 Pi z^3 (1 + z)^(9/2))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["7", "2"], ",", FractionBox["7", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", "4"]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List["24", "+", RowBox[List["113", " ", "z"]], "+", RowBox[List["212", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["13", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["274", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["1125", " ", "\[Pi]", " ", SuperscriptBox["z", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "5"]]]]]], "-", FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List["24", "+", RowBox[List["113", " ", "z"]], "+", RowBox[List["212", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["13", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["274", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["1125", " ", "\[Pi]", " ", SuperscriptBox["z", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["9", "/", "2"]]]]]], "+", FractionBox[RowBox[List["128", " ", RowBox[List["(", RowBox[List["6", "+", RowBox[List["23", " ", "z"]], "-", RowBox[List["2", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["77", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", 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["1125", " ", "\[Pi]", " ", SuperscriptBox["z", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "4"]]]], "+", FractionBox[RowBox[List["64", " ", RowBox[List["(", RowBox[List["12", "+", RowBox[List["55", " ", "z"]], "+", RowBox[List["170", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["137", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["120", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["1125", " ", "\[Pi]", " ", SuperscriptBox["z", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["9", "/", "2"]]]]]]]]]]]]

 MathML Form

 3 F 2 ( 7 2 , 7 2 , 7 2 ; 3 2 , 4 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["7", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "2"], 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[RowBox[List[TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["4", 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] - 32 ( 274 z 4 + 13 z 3 + 212 z 2 + 113 z + 24 ) E ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 1125 π z 3 ( z + 1 ) 9 / 2 - 32 ( 274 z 4 + 13 z 3 + 212 z 2 + 113 z + 24 ) E ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 1125 π z 3 ( z + 1 ) 5 + 128 ( 77 z 3 - 2 z 2 + 23 z + 6 ) K ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 1125 π z 3 ( z + 1 ) 4 + 64 ( 120 z 4 - 137 z 3 + 170 z 2 + 55 z + 12 ) K ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 1125 π z 3 ( z + 1 ) 9 / 2 HypergeometricPFQ 7 2 7 2 7 2 3 2 4 -1 z -1 32 274 z 4 13 z 3 212 z 2 113 z 24 EllipticE z 1 1 2 -1 2 z 1 1 2 1 2 -1 1125 z 3 z 1 9 2 -1 -1 32 274 z 4 13 z 3 212 z 2 113 z 24 EllipticE z 1 1 2 -1 2 z 1 1 2 1 2 -1 1125 z 3 z 1 5 -1 128 77 z 3 -1 2 z 2 23 z 6 EllipticK z 1 1 2 -1 2 z 1 1 2 1 2 -1 1125 z 3 z 1 4 -1 64 120 z 4 -1 137 z 3 170 z 2 55 z 12 EllipticK z 1 1 2 -1 2 z 1 1 2 1 2 -1 1125 z 3 z 1 9 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["7", "2"], ",", FractionBox["7", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", "4"]], "}"]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List["24", "+", RowBox[List["113", " ", "z"]], "+", RowBox[List["212", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["13", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["274", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["1125", " ", "\[Pi]", " ", SuperscriptBox["z", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "5"]]]]]], "-", FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List["24", "+", RowBox[List["113", " ", "z"]], "+", RowBox[List["212", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["13", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["274", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["1125", " ", "\[Pi]", " ", SuperscriptBox["z", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["9", "/", "2"]]]]]], "+", FractionBox[RowBox[List["128", " ", RowBox[List["(", RowBox[List["6", "+", RowBox[List["23", " ", "z"]], "-", RowBox[List["2", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["77", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", 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["1125", " ", "\[Pi]", " ", SuperscriptBox["z", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "4"]]]], "+", FractionBox[RowBox[List["64", " ", RowBox[List["(", RowBox[List["12", "+", RowBox[List["55", " ", "z"]], "+", RowBox[List["170", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["137", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["120", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["1125", " ", "\[Pi]", " ", SuperscriptBox["z", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["9", "/", "2"]]]]]]]]]]]]

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

 2007-05-02