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.aiiq.01

 Input Form

 HypergeometricPFQ[{-(1/2), -(1/2), -(1/2)}, {7/2, 7/2}, z] == (25 Sqrt[1 - z] (-29 - 288 z + 932 z^2))/(49152 z^2) + (25 (Pi^2 + 18 Pi^2 z + 72 Pi^2 z^2 - 16 Pi^2 z^3))/(49152 (-z)^(5/2)) - (25 (-17 - 54 z - 544 z^3) Log[Sqrt[1 - z] + Sqrt[-z]])/ (49152 (-z)^(5/2)) - (25 (1 + 18 z + 72 z^2 - 16 z^3) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/(8192 (-z)^(5/2)) + (25 (1 + 18 z + 72 z^2 - 16 z^3) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/(4096 (-z)^(5/2)) + (25 (1 + 18 z + 72 z^2 - 16 z^3) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/ (4096 (-z)^(5/2)) - (25 (1 + 18 z + 72 z^2 - 16 z^3) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/(4096 (-z)^(5/2))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", RowBox[List["-", FractionBox["1", "2"]]], ",", RowBox[List["-", FractionBox["1", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["7", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["25", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "29"]], "-", RowBox[List["288", " ", "z"]], "+", RowBox[List["932", " ", SuperscriptBox["z", "2"]]]]], ")"]]]], RowBox[List["49152", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "2"], "+", RowBox[List["18", " ", SuperscriptBox["\[Pi]", "2"], " ", "z"]], "+", RowBox[List["72", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["16", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "3"]]]]], ")"]]]], RowBox[List["49152", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "17"]], "-", RowBox[List["54", " ", "z"]], "-", RowBox[List["544", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]]]], RowBox[List["49152", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["18", " ", "z"]], "+", RowBox[List["72", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["16", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]], "2"]]], RowBox[List["8192", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["18", " ", "z"]], "+", RowBox[List["72", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["16", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", 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"]]]]], "]"]]]], RowBox[List["4096", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["18", " ", "z"]], "+", RowBox[List["72", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["16", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List[RowBox[List["-", SqrtBox[RowBox[List["1", "-", "z"]]]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], RowBox[List["4096", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["18", " ", "z"]], "+", RowBox[List["72", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["16", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], RowBox[List["4096", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]]]]]]]]

 MathML Form

 3 F 2 ( - 1 2 , - 1 2 , - 1 2 ; 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[RowBox[List["-", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "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[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] - 25 ( - 16 z 3 + 72 z 2 + 18 z + 1 ) log 2 ( 1 - z + - z ) 8192 ( - z ) 5 / 2 - 25 ( - 544 z 3 - 54 z - 17 ) log ( 1 - z + - z ) 49152 ( - z ) 5 / 2 + 25 ( - 16 z 3 + 72 z 2 + 18 z + 1 ) log ( 1 - z + - z + 1 ) log ( 1 - z + - z ) 4096 ( - z ) 5 / 2 + 25 1 - z ( 932 z 2 - 288 z - 29 ) 49152 z 2 + 25 ( - 16 π 2 z 3 + 72 π 2 z 2 + 18 π 2 z + π 2 ) 49152 ( - z ) 5 / 2 + 25 ( - 16 z 3 + 72 z 2 + 18 z + 1 ) Li PolyLog 2 ( - 1 - z - - z ) 4096 ( - z ) 5 / 2 - 25 ( - 16 z 3 + 72 z 2 + 18 z + 1 ) Li PolyLog 2 ( - 1 - z - - z + 1 ) 4096 ( - z ) 5 / 2 HypergeometricPFQ -1 1 2 -1 1 2 -1 1 2 7 2 7 2 z -1 25 -16 z 3 72 z 2 18 z 1 1 -1 z 1 2 -1 z 1 2 2 8192 -1 z 5 2 -1 -1 25 -544 z 3 -1 54 z -17 1 -1 z 1 2 -1 z 1 2 49152 -1 z 5 2 -1 25 -16 z 3 72 z 2 18 z 1 1 -1 z 1 2 -1 z 1 2 1 1 -1 z 1 2 -1 z 1 2 4096 -1 z 5 2 -1 25 1 -1 z 1 2 932 z 2 -1 288 z -29 49152 z 2 -1 25 -16 2 z 3 72 2 z 2 18 2 z 2 49152 -1 z 5 2 -1 25 -16 z 3 72 z 2 18 z 1 PolyLog 2 -1 1 -1 z 1 2 -1 -1 z 1 2 4096 -1 z 5 2 -1 -1 25 -16 z 3 72 z 2 18 z 1 PolyLog 2 -1 1 -1 z 1 2 -1 -1 z 1 2 1 4096 -1 z 5 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", RowBox[List["-", FractionBox["1", "2"]]], ",", RowBox[List["-", FractionBox["1", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["7", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["25", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "29"]], "-", RowBox[List["288", " ", "z"]], "+", RowBox[List["932", " ", SuperscriptBox["z", "2"]]]]], ")"]]]], RowBox[List["49152", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "2"], "+", RowBox[List["18", " ", SuperscriptBox["\[Pi]", "2"], " ", "z"]], "+", RowBox[List["72", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["16", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "3"]]]]], ")"]]]], RowBox[List["49152", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "17"]], "-", RowBox[List["54", " ", "z"]], "-", RowBox[List["544", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]]]], RowBox[List["49152", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["18", " ", "z"]], "+", RowBox[List["72", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["16", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]], "2"]]], RowBox[List["8192", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["18", " ", "z"]], "+", RowBox[List["72", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["16", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", 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"]]]]], "]"]]]], RowBox[List["4096", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["18", " ", "z"]], "+", RowBox[List["72", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["16", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List[RowBox[List["-", SqrtBox[RowBox[List["1", "-", "z"]]]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], RowBox[List["4096", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["18", " ", "z"]], "+", RowBox[List["72", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["16", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], RowBox[List["4096", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]]]]]]]]

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

 2007-05-02