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/07.27.03.1992.01

 Input Form

 HypergeometricPFQ[{-(7/2), -(7/2), 3}, {1, 4}, -z] == (1/(19324305 Pi z^3)) (4 (-2240 + 560 z - 315 z^2 + 30781076 z^3 - 177643586 z^4 + 142003044 z^5 - 15292827 z^6) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(19324305 Pi z^3)) (4 Sqrt[1 + z] (-2240 + 560 z - 315 z^2 + 30781076 z^3 - 177643586 z^4 + 142003044 z^5 - 15292827 z^6) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(19324305 Pi z^3)) (32 (280 - 35 z - 2415525 z^2 + 17741258 z^3 - 279562 z^4 - 17727687 z^5 + 2708343 z^6) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(19324305 Pi z^3)) (8 Sqrt[1 + z] (1120 - 420 z + 9662415 z^2 - 101746108 z^3 + 178761834 z^4 - 71092296 z^5 + 4459455 z^6) 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"]]], ",", "3"]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", "4"]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", RowBox[List["19324305", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2240"]], "+", RowBox[List["560", " ", "z"]], "-", RowBox[List["315", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["30781076", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["177643586", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["142003044", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["15292827", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", 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["19324305", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], RowBox[List["(", RowBox[List["4", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2240"]], "+", RowBox[List["560", " ", "z"]], "-", RowBox[List["315", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["30781076", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["177643586", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["142003044", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["15292827", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", 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["19324305", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], RowBox[List["(", RowBox[List["32", " ", RowBox[List["(", RowBox[List["280", "-", RowBox[List["35", " ", "z"]], "-", RowBox[List["2415525", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["17741258", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["279562", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["17727687", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["2708343", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", 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["19324305", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], RowBox[List["(", RowBox[List["8", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["1120", "-", RowBox[List["420", " ", "z"]], "+", RowBox[List["9662415", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["101746108", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["178761834", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["71092296", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["4459455", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", 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 , 3 ; 1 , 4 ; - 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["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox["1", 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] 1 19324305 π z 3 4 z + 1 ( - 15292827 z 6 + 142003044 z 5 - 177643586 z 4 + 30781076 z 3 - 315 z 2 + 560 z - 2240 ) E ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) + 1 19324305 π z 3 4 ( - 15292827 z 6 + 142003044 z 5 - 177643586 z 4 + 30781076 z 3 - 315 z 2 + 560 z - 2240 ) E ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) + 1 19324305 π z 3 32 ( 2708343 z 6 - 17727687 z 5 - 279562 z 4 + 17741258 z 3 - 2415525 z 2 - 35 z + 280 ) K ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) + 1 19324305 π z 3 ( 8 z + 1 ( 4459455 z 6 - 71092296 z 5 + 178761834 z 4 - 101746108 z 3 + 9662415 z 2 - 420 z + 1120 ) K ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) ) HypergeometricPFQ -1 7 2 -1 7 2 3 1 4 -1 z 1 19324305 z 3 -1 4 z 1 1 2 -15292827 z 6 142003044 z 5 -1 177643586 z 4 30781076 z 3 -1 315 z 2 560 z -2240 EllipticE z 1 1 2 -1 2 z 1 1 2 1 2 -1 1 19324305 z 3 -1 4 -15292827 z 6 142003044 z 5 -1 177643586 z 4 30781076 z 3 -1 315 z 2 560 z -2240 EllipticE z 1 1 2 -1 2 z 1 1 2 1 2 -1 1 19324305 z 3 -1 32 2708343 z 6 -1 17727687 z 5 -1 279562 z 4 17741258 z 3 -1 2415525 z 2 -1 35 z 280 EllipticK z 1 1 2 -1 2 z 1 1 2 1 2 -1 1 19324305 z 3 -1 8 z 1 1 2 4459455 z 6 -1 71092296 z 5 178761834 z 4 -1 101746108 z 3 9662415 z 2 -1 420 z 1120 EllipticK z 1 1 2 -1 2 z 1 1 2 1 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"]]], ",", "3"]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", "4"]], "}"]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2240"]], "+", RowBox[List["560", " ", "z"]], "-", RowBox[List["315", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["30781076", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["177643586", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["142003044", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["15292827", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", 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["19324305", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], "+", FractionBox[RowBox[List["4", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2240"]], "+", RowBox[List["560", " ", "z"]], "-", RowBox[List["315", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["30781076", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["177643586", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["142003044", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["15292827", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", 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["19324305", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], "+", FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List["280", "-", RowBox[List["35", " ", "z"]], "-", RowBox[List["2415525", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["17741258", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["279562", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["17727687", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["2708343", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", 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["19324305", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], "+", FractionBox[RowBox[List["8", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["1120", "-", RowBox[List["420", " ", "z"]], "+", RowBox[List["9662415", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["101746108", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["178761834", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["71092296", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["4459455", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", 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["19324305", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]]]]]]]]

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

 2007-05-02