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/07.27.03.1021.01

 Input Form

 HypergeometricPFQ[{-(7/2), -(7/2), -(7/2)}, {-(1/2), 3/2}, z] == -((1225 (105 Pi^2 (-z)^(3/2) + 112 Pi^2 (-z)^(5/2) + 4 Pi^2 (-z)^(7/2)))/ 16384) + (Sqrt[1 - z] (3017103 + 164853898 z - 698147960 z^2 + 78270544 z^3))/3145728 + (35 (1225 + 156800 z - 470400 z^2 - 4365312 z^3 + 372864 z^4) Log[Sqrt[1 - z] + Sqrt[-z]])/(1048576 Sqrt[-z]) + (3675 (105 (-z)^(3/2) + 112 (-z)^(5/2) + 4 (-z)^(7/2)) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/8192 - (1/4096) (3675 (105 (-z)^(3/2) + 112 (-z)^(5/2) + 4 (-z)^(7/2)) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]]) - (3675 (105 (-z)^(3/2) + 112 (-z)^(5/2) + 4 (-z)^(7/2)) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/4096 + (3675 (105 (-z)^(3/2) + 112 (-z)^(5/2) + 4 (-z)^(7/2)) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/4096

 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["7", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", FractionBox["3", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["1225", " ", RowBox[List["(", RowBox[List[RowBox[List["105", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["112", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["4", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["7", "/", "2"]]]]]]], ")"]]]], "16384"]]], "+", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["3017103", "+", RowBox[List["164853898", " ", "z"]], "-", RowBox[List["698147960", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["78270544", " ", SuperscriptBox["z", "3"]]]]], ")"]]]], "3145728"], "+", FractionBox[RowBox[List["35", " ", RowBox[List["(", RowBox[List["1225", "+", RowBox[List["156800", " ", "z"]], "-", RowBox[List["470400", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4365312", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["372864", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]]]], RowBox[List["1048576", " ", SqrtBox[RowBox[List["-", "z"]]]]]], "+", FractionBox[RowBox[List["3675", " ", RowBox[List["(", RowBox[List[RowBox[List["105", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["112", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]], "2"]]], "8192"], "-", RowBox[List[FractionBox["1", "4096"], RowBox[List["3675", " ", RowBox[List["(", RowBox[List[RowBox[List["105", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["112", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["7", "/", "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"]]]]], "]"]]]]]], "-", FractionBox[RowBox[List["3675", " ", RowBox[List["(", RowBox[List[RowBox[List["105", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["112", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List[RowBox[List["-", SqrtBox[RowBox[List["1", "-", "z"]]]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], "4096"], "+", FractionBox[RowBox[List["3675", " ", RowBox[List["(", RowBox[List[RowBox[List["105", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["112", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], "4096"]]]]]]]

 MathML Form

 3 F 2 ( - 7 2 , - 7 2 , - 7 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["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["7", "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[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] 3675 ( 4 ( - z ) 7 / 2 + 112 ( - z ) 5 / 2 + 105 ( - z ) 3 / 2 ) log 2 ( 1 - z + - z ) 8192 + 35 ( 372864 z 4 - 4365312 z 3 - 470400 z 2 + 156800 z + 1225 ) log ( 1 - z + - z ) 1048576 - z - 3675 ( 4 ( - z ) 7 / 2 + 112 ( - z ) 5 / 2 + 105 ( - z ) 3 / 2 ) log ( 1 - z + - z + 1 ) log ( 1 - z + - z ) 4096 - 1225 ( 4 π 2 ( - z ) 7 / 2 + 112 π 2 ( - z ) 5 / 2 + 105 π 2 ( - z ) 3 / 2 ) 16384 + 1 - z ( 78270544 z 3 - 698147960 z 2 + 164853898 z + 3017103 ) 3145728 - 3675 ( 4 ( - z ) 7 / 2 + 112 ( - z ) 5 / 2 + 105 ( - z ) 3 / 2 ) Li PolyLog 2 ( - 1 - z - - z ) 4096 + 3675 ( 4 ( - z ) 7 / 2 + 112 ( - z ) 5 / 2 + 105 ( - z ) 3 / 2 ) Li PolyLog 2 ( - 1 - z - - z + 1 ) 4096 HypergeometricPFQ -1 7 2 -1 7 2 -1 7 2 -1 1 2 3 2 z 3675 4 -1 z 7 2 112 -1 z 5 2 105 -1 z 3 2 1 -1 z 1 2 -1 z 1 2 2 8192 -1 35 372864 z 4 -1 4365312 z 3 -1 470400 z 2 156800 z 1225 1 -1 z 1 2 -1 z 1 2 1048576 -1 z 1 2 -1 -1 3675 4 -1 z 7 2 112 -1 z 5 2 105 -1 z 3 2 1 -1 z 1 2 -1 z 1 2 1 1 -1 z 1 2 -1 z 1 2 4096 -1 -1 1225 4 2 -1 z 7 2 112 2 -1 z 5 2 105 2 -1 z 3 2 16384 -1 1 -1 z 1 2 78270544 z 3 -1 698147960 z 2 164853898 z 3017103 3145728 -1 -1 3675 4 -1 z 7 2 112 -1 z 5 2 105 -1 z 3 2 PolyLog 2 -1 1 -1 z 1 2 -1 -1 z 1 2 4096 -1 3675 4 -1 z 7 2 112 -1 z 5 2 105 -1 z 3 2 PolyLog 2 -1 1 -1 z 1 2 -1 -1 z 1 2 1 4096 -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["7", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", FractionBox["3", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["1225", " ", RowBox[List["(", RowBox[List[RowBox[List["105", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["112", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["4", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["7", "/", "2"]]]]]]], ")"]]]], "16384"]]], "+", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["3017103", "+", RowBox[List["164853898", " ", "z"]], "-", RowBox[List["698147960", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["78270544", " ", SuperscriptBox["z", "3"]]]]], ")"]]]], "3145728"], "+", FractionBox[RowBox[List["35", " ", RowBox[List["(", RowBox[List["1225", "+", RowBox[List["156800", " ", "z"]], "-", RowBox[List["470400", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4365312", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["372864", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]]]], RowBox[List["1048576", " ", SqrtBox[RowBox[List["-", "z"]]]]]], "+", FractionBox[RowBox[List["3675", " ", RowBox[List["(", RowBox[List[RowBox[List["105", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["112", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]], "2"]]], "8192"], "-", FractionBox[RowBox[List["3675", " ", RowBox[List["(", RowBox[List[RowBox[List["105", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["112", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["7", "/", "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"]]]]], "]"]]]], "4096"], "-", FractionBox[RowBox[List["3675", " ", RowBox[List["(", RowBox[List[RowBox[List["105", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["112", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List[RowBox[List["-", SqrtBox[RowBox[List["1", "-", "z"]]]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], "4096"], "+", FractionBox[RowBox[List["3675", " ", RowBox[List["(", RowBox[List[RowBox[List["105", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["112", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], "4096"]]]]]]]

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

 2007-05-02