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.a7py.01

 Input Form

 HypergeometricPFQ[{-(5/2), -(5/2), -(5/2)}, {1/2, 3/2}, z] == (25 (45 Pi^2 Sqrt[-z] + 120 Pi^2 (-z)^(3/2) + 8 Pi^2 (-z)^(5/2)))/4096 + (Sqrt[1 - z] (11913 - 179231 z + 43358 z^2))/12288 - (5 (-25 + 2025 z + 7800 z^2 - 1536 z^3) Log[Sqrt[1 - z] + Sqrt[-z]])/ (4096 Sqrt[-z]) - (75 (45 Sqrt[-z] + 120 (-z)^(3/2) + 8 (-z)^(5/2)) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/2048 + (75 (45 Sqrt[-z] + 120 (-z)^(3/2) + 8 (-z)^(5/2)) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/1024 + (75 (45 Sqrt[-z] + 120 (-z)^(3/2) + 8 (-z)^(5/2)) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/1024 - (75 (45 Sqrt[-z] + 120 (-z)^(3/2) + 8 (-z)^(5/2)) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/1024

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["3", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List[RowBox[List["45", " ", SuperscriptBox["\[Pi]", "2"], " ", SqrtBox[RowBox[List["-", "z"]]]]], "+", RowBox[List["120", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["8", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]]], ")"]]]], "4096"], "+", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["11913", "-", RowBox[List["179231", " ", "z"]], "+", RowBox[List["43358", " ", SuperscriptBox["z", "2"]]]]], ")"]]]], "12288"], "-", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "25"]], "+", RowBox[List["2025", " ", "z"]], "+", RowBox[List["7800", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1536", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]]]], RowBox[List["4096", " ", SqrtBox[RowBox[List["-", "z"]]]]]], "-", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List[RowBox[List["45", " ", SqrtBox[RowBox[List["-", "z"]]]]], "+", RowBox[List["120", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]], "2"]]], "2048"], "+", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List[RowBox[List["45", " ", SqrtBox[RowBox[List["-", "z"]]]]], "+", RowBox[List["120", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]]]], "1024"], "+", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List[RowBox[List["45", " ", SqrtBox[RowBox[List["-", "z"]]]]], "+", RowBox[List["120", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List[RowBox[List["-", SqrtBox[RowBox[List["1", "-", "z"]]]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], "1024"], "-", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List[RowBox[List["45", " ", SqrtBox[RowBox[List["-", "z"]]]]], "+", RowBox[List["120", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], "1024"]]]]]]]

 MathML Form

 3 F 2 ( - 5 2 , - 5 2 , - 5 2 ; 1 2 , 3 2 ; 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["5", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["5", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["5", "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["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "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 ( 8 ( - z ) 5 / 2 + 120 ( - z ) 3 / 2 + 45 - z ) log 2 ( 1 - z + - z ) 2048 - 5 ( - 1536 z 3 + 7800 z 2 + 2025 z - 25 ) log ( 1 - z + - z ) 4096 - z + 75 ( 8 ( - z ) 5 / 2 + 120 ( - z ) 3 / 2 + 45 - z ) log ( 1 - z + - z + 1 ) log ( 1 - z + - z ) 1024 + 25 ( 8 π 2 ( - z ) 5 / 2 + 120 π 2 ( - z ) 3 / 2 + 45 π 2 - z ) 4096 + 1 - z ( 43358 z 2 - 179231 z + 11913 ) 12288 + 75 ( 8 ( - z ) 5 / 2 + 120 ( - z ) 3 / 2 + 45 - z ) Li PolyLog 2 ( - 1 - z - - z ) 1024 - 75 ( 8 ( - z ) 5 / 2 + 120 ( - z ) 3 / 2 + 45 - z ) Li PolyLog 2 ( - 1 - z - - z + 1 ) 1024 HypergeometricPFQ -1 5 2 -1 5 2 -1 5 2 1 2 3 2 z -1 75 8 -1 z 5 2 120 -1 z 3 2 45 -1 z 1 2 1 -1 z 1 2 -1 z 1 2 2 2048 -1 -1 5 -1536 z 3 7800 z 2 2025 z -25 1 -1 z 1 2 -1 z 1 2 4096 -1 z 1 2 -1 75 8 -1 z 5 2 120 -1 z 3 2 45 -1 z 1 2 1 -1 z 1 2 -1 z 1 2 1 1 -1 z 1 2 -1 z 1 2 1024 -1 25 8 2 -1 z 5 2 120 2 -1 z 3 2 45 2 -1 z 1 2 4096 -1 1 -1 z 1 2 43358 z 2 -1 179231 z 11913 12288 -1 75 8 -1 z 5 2 120 -1 z 3 2 45 -1 z 1 2 PolyLog 2 -1 1 -1 z 1 2 -1 -1 z 1 2 1024 -1 -1 75 8 -1 z 5 2 120 -1 z 3 2 45 -1 z 1 2 PolyLog 2 -1 1 -1 z 1 2 -1 -1 z 1 2 1 1024 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]], ",", RowBox[List["-", FractionBox["5", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["3", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List[RowBox[List["45", " ", SuperscriptBox["\[Pi]", "2"], " ", SqrtBox[RowBox[List["-", "z"]]]]], "+", RowBox[List["120", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["8", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]]], ")"]]]], "4096"], "+", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["11913", "-", RowBox[List["179231", " ", "z"]], "+", RowBox[List["43358", " ", SuperscriptBox["z", "2"]]]]], ")"]]]], "12288"], "-", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "25"]], "+", RowBox[List["2025", " ", "z"]], "+", RowBox[List["7800", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1536", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]]]], RowBox[List["4096", " ", SqrtBox[RowBox[List["-", "z"]]]]]], "-", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List[RowBox[List["45", " ", SqrtBox[RowBox[List["-", "z"]]]]], "+", RowBox[List["120", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]], "2"]]], "2048"], "+", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List[RowBox[List["45", " ", SqrtBox[RowBox[List["-", "z"]]]]], "+", RowBox[List["120", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]]]], "1024"], "+", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List[RowBox[List["45", " ", SqrtBox[RowBox[List["-", "z"]]]]], "+", RowBox[List["120", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List[RowBox[List["-", SqrtBox[RowBox[List["1", "-", "z"]]]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], "1024"], "-", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List[RowBox[List["45", " ", SqrtBox[RowBox[List["-", "z"]]]]], "+", RowBox[List["120", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], "1024"]]]]]]]

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

 2007-05-02