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/07.27.03.2152.01

 Input Form

 HypergeometricPFQ[{-(7/2), -(7/2), 7/2}, {5/2, 3}, -z] == -((1/(1715175 Pi z^2)) (16 (70 + 6335 z - 602400 z^2 + 2294882 z^3 - 1506878 z^4 + 144327 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])) - (1/(1715175 Pi z^2)) (16 Sqrt[1 + z] (70 + 6335 z - 602400 z^2 + 2294882 z^3 - 1506878 z^4 + 144327 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(1715175 Pi z^2)) (32 Sqrt[1 + z] (35 + 217560 z - 1473630 z^2 + 2093236 z^3 - 728781 z^4 + 41580 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(1715175 Pi z^2)) (32 (35 - 211225 z + 871230 z^2 + 201646 z^3 - 778097 z^4 + 102747 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", RowBox[List["-", FractionBox["7", "2"]]], ",", FractionBox["7", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "2"], ",", "3"]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List["1715175", " ", "\[Pi]", " ", SuperscriptBox["z", "2"]]]], RowBox[List["16", " ", RowBox[List["(", RowBox[List["70", "+", RowBox[List["6335", " ", "z"]], "-", RowBox[List["602400", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2294882", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1506878", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["144327", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", 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[FractionBox["1", RowBox[List["1715175", " ", "\[Pi]", " ", SuperscriptBox["z", "2"]]]], RowBox[List["(", RowBox[List["16", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["70", "+", RowBox[List["6335", " ", "z"]], "-", RowBox[List["602400", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2294882", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1506878", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["144327", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", 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[FractionBox["1", RowBox[List["1715175", " ", "\[Pi]", " ", SuperscriptBox["z", "2"]]]], RowBox[List["(", RowBox[List["32", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["35", "+", RowBox[List["217560", " ", "z"]], "-", RowBox[List["1473630", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2093236", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["728781", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["41580", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", 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[FractionBox["1", RowBox[List["1715175", " ", "\[Pi]", " ", SuperscriptBox["z", "2"]]]], RowBox[List["32", " ", RowBox[List["(", RowBox[List["35", "-", RowBox[List["211225", " ", "z"]], "+", RowBox[List["871230", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["201646", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["778097", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["102747", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", 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"]], "]"]]]]]]]]]]]]

 MathML Form

 3 F 2 ( - 7 2 , - 7 2 , 7 2 ; 5 2 , 3 ; - 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["7", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", 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["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", 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] - 16 z + 1 ( 144327 z 5 - 1506878 z 4 + 2294882 z 3 - 602400 z 2 + 6335 z + 70 ) E ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 1715175 π z 2 - 16 ( 144327 z 5 - 1506878 z 4 + 2294882 z 3 - 602400 z 2 + 6335 z + 70 ) E ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 1715175 π z 2 + 32 z + 1 ( 41580 z 5 - 728781 z 4 + 2093236 z 3 - 1473630 z 2 + 217560 z + 35 ) K ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 1715175 π z 2 + 32 ( 102747 z 5 - 778097 z 4 + 201646 z 3 + 871230 z 2 - 211225 z + 35 ) K ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 1715175 π z 2 HypergeometricPFQ -1 7 2 -1 7 2 7 2 5 2 3 -1 z -1 16 z 1 1 2 144327 z 5 -1 1506878 z 4 2294882 z 3 -1 602400 z 2 6335 z 70 EllipticE z 1 1 2 -1 2 z 1 1 2 1 2 -1 1715175 z 2 -1 -1 16 144327 z 5 -1 1506878 z 4 2294882 z 3 -1 602400 z 2 6335 z 70 EllipticE z 1 1 2 -1 2 z 1 1 2 1 2 -1 1715175 z 2 -1 32 z 1 1 2 41580 z 5 -1 728781 z 4 2093236 z 3 -1 1473630 z 2 217560 z 35 EllipticK z 1 1 2 -1 2 z 1 1 2 1 2 -1 1715175 z 2 -1 32 102747 z 5 -1 778097 z 4 201646 z 3 871230 z 2 -1 211225 z 35 EllipticK z 1 1 2 -1 2 z 1 1 2 1 2 -1 1715175 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", RowBox[List["-", FractionBox["7", "2"]]], ",", FractionBox["7", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "2"], ",", "3"]], "}"]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["16", " ", RowBox[List["(", RowBox[List["70", "+", RowBox[List["6335", " ", "z"]], "-", RowBox[List["602400", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2294882", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1506878", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["144327", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", 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["1715175", " ", "\[Pi]", " ", SuperscriptBox["z", "2"]]]]]], "-", FractionBox[RowBox[List["16", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["70", "+", RowBox[List["6335", " ", "z"]], "-", RowBox[List["602400", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2294882", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1506878", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["144327", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", 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["1715175", " ", "\[Pi]", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["32", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["35", "+", RowBox[List["217560", " ", "z"]], "-", RowBox[List["1473630", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2093236", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["728781", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["41580", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", 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["1715175", " ", "\[Pi]", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List["35", "-", RowBox[List["211225", " ", "z"]], "+", RowBox[List["871230", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["201646", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["778097", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["102747", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", 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["1715175", " ", "\[Pi]", " ", SuperscriptBox["z", "2"]]]]]]]]]]

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

 2007-05-02