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/07.27.03.1286.01

 Input Form

 HypergeometricPFQ[{-(7/2), -(7/2), -(1/2)}, {-(1/2), 4}, -z] == -((1/(19324305 Pi z^3)) (32 (280 + 5845 z + 88025 z^2 - 2963342 z^3 + 6086186 z^4 - 2500919 z^5 + 163573 z^6) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])) - (1/(19324305 Pi z^3)) (32 Sqrt[1 + z] (280 + 5845 z + 88025 z^2 - 2963342 z^3 + 6086186 z^4 - 2500919 z^5 + 163573 z^6) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(19324305 Pi z^3)) (256 (35 + 735 z - 290850 z^2 + 480126 z^3 + 390639 z^4 - 351405 z^5 + 29632 z^6) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(19324305 Pi z^3)) (64 Sqrt[1 + z] (140 + 2905 z + 1251425 z^2 - 4883846 z^3 + 4523630 z^4 - 1095299 z^5 + 45045 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"]]], ",", RowBox[List["-", FractionBox["1", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", "4"]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List["19324305", " ", "\[Pi]", " ", SuperscriptBox["z", "3"]]]], RowBox[List["(", RowBox[List["32", " ", RowBox[List["(", RowBox[List["280", "+", RowBox[List["5845", " ", "z"]], "+", RowBox[List["88025", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2963342", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["6086186", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["2500919", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["163573", " ", 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", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["280", "+", RowBox[List["5845", " ", "z"]], "+", RowBox[List["88025", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2963342", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["6086186", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["2500919", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["163573", " ", 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["256", " ", RowBox[List["(", RowBox[List["35", "+", RowBox[List["735", " ", "z"]], "-", RowBox[List["290850", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["480126", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["390639", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["351405", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["29632", " ", 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["64", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["140", "+", RowBox[List["2905", " ", "z"]], "+", RowBox[List["1251425", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4883846", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["4523630", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1095299", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["45045", " ", 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 , - 1 2 ; - 1 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[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[RowBox[List["-", FractionBox["1", "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["1", "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] - 1 19324305 π z 3 32 z + 1 ( 163573 z 6 - 2500919 z 5 + 6086186 z 4 - 2963342 z 3 + 88025 z 2 + 5845 z + 280 ) E ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) - 1 19324305 π z 3 32 ( 163573 z 6 - 2500919 z 5 + 6086186 z 4 - 2963342 z 3 + 88025 z 2 + 5845 z + 280 ) E ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) + 256 ( 29632 z 6 - 351405 z 5 + 390639 z 4 + 480126 z 3 - 290850 z 2 + 735 z + 35 ) K ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 19324305 π z 3 + 1 19324305 π z 3 64 z + 1 ( 45045 z 6 - 1095299 z 5 + 4523630 z 4 - 4883846 z 3 + 1251425 z 2 + 2905 z + 140 ) K ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) HypergeometricPFQ -1 7 2 -1 7 2 -1 1 2 -1 1 2 4 -1 z -1 1 19324305 z 3 -1 32 z 1 1 2 163573 z 6 -1 2500919 z 5 6086186 z 4 -1 2963342 z 3 88025 z 2 5845 z 280 EllipticE z 1 1 2 -1 2 z 1 1 2 1 2 -1 -1 1 19324305 z 3 -1 32 163573 z 6 -1 2500919 z 5 6086186 z 4 -1 2963342 z 3 88025 z 2 5845 z 280 EllipticE z 1 1 2 -1 2 z 1 1 2 1 2 -1 256 29632 z 6 -1 351405 z 5 390639 z 4 480126 z 3 -1 290850 z 2 735 z 35 EllipticK z 1 1 2 -1 2 z 1 1 2 1 2 -1 19324305 z 3 -1 1 19324305 z 3 -1 64 z 1 1 2 45045 z 6 -1 1095299 z 5 4523630 z 4 -1 4883846 z 3 1251425 z 2 2905 z 140 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"]]], ",", RowBox[List["-", FractionBox["1", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", "4"]], "}"]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List["280", "+", RowBox[List["5845", " ", "z"]], "+", RowBox[List["88025", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2963342", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["6086186", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["2500919", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["163573", " ", 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", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["280", "+", RowBox[List["5845", " ", "z"]], "+", RowBox[List["88025", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2963342", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["6086186", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["2500919", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["163573", " ", 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["256", " ", RowBox[List["(", RowBox[List["35", "+", RowBox[List["735", " ", "z"]], "-", RowBox[List["290850", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["480126", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["390639", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["351405", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["29632", " ", 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["64", " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["(", RowBox[List["140", "+", RowBox[List["2905", " ", "z"]], "+", RowBox[List["1251425", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4883846", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["4523630", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1095299", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["45045", " ", 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