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.auc0.01

 Input Form

 HypergeometricPFQ[{5/2, 3, 3}, {7/2, 7/2}, z] == (75 I (-3 Pi^2 + 4 I Sqrt[z] + 3 Pi^2 z))/(256 (-1 + z) z^(5/2)) + (75 Sqrt[1 - z] (-4 + 5 z) ArcSin[Sqrt[z]])/(64 (-1 + z)^2 z^(5/2)) - (75 Sqrt[1 - z] (-3 + 4 z) Log[1 - E^(I ArcSin[Sqrt[z]])])/ (64 (-1 + z)^2 z^2) + (75 Sqrt[1 - z] (-3 + 4 z) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (64 (-1 + z)^2 z^2) + (225 ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (64 z^(5/2)) + (75 Sqrt[1 - z] (-3 + 4 z) Log[1 + E^(I ArcSin[Sqrt[z]])])/ (64 (-1 + z)^2 z^2) + (225 I PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/ (64 z^(5/2)) - (225 I PolyLog[2, E^(I ArcSin[Sqrt[z]])])/(64 z^(5/2))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "2"], ",", "3", ",", "3"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["7", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["75", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", SuperscriptBox["\[Pi]", "2"]]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", SqrtBox["z"]]], "+", RowBox[List["3", " ", SuperscriptBox["\[Pi]", "2"], " ", "z"]]]], ")"]]]], RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List["75", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["5", " ", "z"]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]], RowBox[List["64", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["75", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["64", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["75", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]], "]"]]]], RowBox[List["64", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["225", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]], "]"]]]], RowBox[List["64", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List["75", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["64", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["225", " ", "\[ImaginaryI]", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]]], "]"]]]], RowBox[List["64", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["225", " ", "\[ImaginaryI]", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["64", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]]]]]]]

 MathML Form

 3 F 2 ( 5 2 , 3 , 3 ; 7 2 , 7 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", 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[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["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] 75 ( 3 π 2 z + 4 z - 3 π 2 ) 256 ( z - 1 ) z 5 / 2 + 75 1 - z ( 5 z - 4 ) sin - 1 ( z ) 64 ( z - 1 ) 2 z 5 / 2 - 75 1 - z ( 4 z - 3 ) log ( 1 - sin - 1 ( z ) ) 64 ( z - 1 ) 2 z 2 + 75 1 - z ( 4 z - 3 ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 64 ( z - 1 ) 2 z 2 + 225 sin - 1 ( z ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 64 z 5 / 2 + 75 1 - z ( 4 z - 3 ) log ( 1 + sin - 1 ( z ) ) 64 ( z - 1 ) 2 z 2 + 225 Li PolyLog 2 ( - sin - 1 ( z ) ) 64 z 5 / 2 - 225 Li PolyLog 2 ( sin - 1 ( z ) ) 64 z 5 / 2 HypergeometricPFQ 5 2 3 3 7 2 7 2 z 75 3 2 z 4 z 1 2 -1 3 2 256 z -1 z 5 2 -1 75 1 -1 z 1 2 5 z -4 z 1 2 64 z -1 2 z 5 2 -1 -1 75 1 -1 z 1 2 4 z -3 1 -1 z 1 2 64 z -1 2 z 2 -1 75 1 -1 z 1 2 4 z -3 1 -1 z 1 2 1 z 1 2 -1 64 z -1 2 z 2 -1 225 z 1 2 1 -1 z 1 2 1 z 1 2 -1 64 z 5 2 -1 75 1 -1 z 1 2 4 z -3 1 z 1 2 64 z -1 2 z 2 -1 225 PolyLog 2 -1 z 1 2 64 z 5 2 -1 -1 225 PolyLog 2 z 1 2 64 z 5 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "2"], ",", "3", ",", "3"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["7", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["75", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", SuperscriptBox["\[Pi]", "2"]]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", SqrtBox["z"]]], "+", RowBox[List["3", " ", SuperscriptBox["\[Pi]", "2"], " ", "z"]]]], ")"]]]], RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List["75", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["5", " ", "z"]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]], RowBox[List["64", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["75", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["64", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["75", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]], "]"]]]], RowBox[List["64", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["225", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]], "]"]]]], RowBox[List["64", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List["75", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["4", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["64", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["225", " ", "\[ImaginaryI]", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]]], "]"]]]], RowBox[List["64", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["225", " ", "\[ImaginaryI]", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["64", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]]]]]]]

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

 2007-05-02