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/07.27.03.1092.01

 Input Form

 HypergeometricPFQ[{-(7/2), -(7/2), -(5/2)}, {-(3/2), 5/2}, z] == (1225 Pi^2 (-z)^(5/2))/2048 - (Sqrt[1 - z] (-2205 - 1427334 z - 10006664 z^2 - 24877360 z^3 + 1070208 z^4))/(1572864 z) - (35 (-21 + 1400 z + 33600 z^2 + 134400 z^3 + 169344 z^4 - 3072 z^5) Log[Sqrt[1 - z] + Sqrt[-z]])/(524288 (-z)^(3/2)) - (3675 (-z)^(5/2) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/1024 + (3675/512) (-z)^(5/2) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]] + (3675/512) (-z)^(5/2) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]] - (3675/512) (-z)^(5/2) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]]

 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["5", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], ",", FractionBox["5", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["1225", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "2048"], "-", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2205"]], "-", RowBox[List["1427334", " ", "z"]], "-", RowBox[List["10006664", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["24877360", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1070208", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], RowBox[List["1572864", " ", "z"]]], "-", FractionBox[RowBox[List["35", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "21"]], "+", RowBox[List["1400", " ", "z"]], "+", RowBox[List["33600", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["134400", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["169344", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["3072", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]]]], RowBox[List["524288", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "-", FractionBox[RowBox[List["3675", " ", 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"]]], "1024"], "+", RowBox[List[FractionBox["3675", "512"], " ", 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"]]]]], "]"]]]], "+", RowBox[List[FractionBox["3675", "512"], " ", 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"]]]]]]], "]"]]]], "-", RowBox[List[FractionBox["3675", "512"], " ", 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"]]]]]]], "]"]]]]]]]]]]

 MathML Form

 3 F 2 ( - 7 2 , - 7 2 , - 5 2 ; - 3 2 , 5 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["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[RowBox[List["-", FractionBox["3", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "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 log 2 ( 1 - z + - z ) ( - z ) 5 / 2 1024 + 3675 512 log ( 1 - z + - z ) log ( 1 - z + - z + 1 ) ( - z ) 5 / 2 + 3675 512 Li PolyLog 2 ( - 1 - z - - z ) ( - z ) 5 / 2 - 3675 512 Li PolyLog 2 ( - 1 - z - - z + 1 ) ( - z ) 5 / 2 + 1225 π 2 ( - z ) 5 / 2 2048 - 1 - z ( 1070208 z 4 - 24877360 z 3 - 10006664 z 2 - 1427334 z - 2205 ) 1572864 z - 35 ( - 3072 z 5 + 169344 z 4 + 134400 z 3 + 33600 z 2 + 1400 z - 21 ) log ( 1 - z + - z ) 524288 ( - z ) 3 / 2 HypergeometricPFQ -1 7 2 -1 7 2 -1 5 2 -1 3 2 5 2 z -1 3675 1 -1 z 1 2 -1 z 1 2 2 -1 z 5 2 1024 -1 3675 512 1 -1 z 1 2 -1 z 1 2 1 -1 z 1 2 -1 z 1 2 1 -1 z 5 2 3675 512 PolyLog 2 -1 1 -1 z 1 2 -1 -1 z 1 2 -1 z 5 2 -1 3675 512 PolyLog 2 -1 1 -1 z 1 2 -1 -1 z 1 2 1 -1 z 5 2 1225 2 -1 z 5 2 2048 -1 -1 1 -1 z 1 2 1070208 z 4 -1 24877360 z 3 -1 10006664 z 2 -1 1427334 z -2205 1572864 z -1 -1 35 -3072 z 5 169344 z 4 134400 z 3 33600 z 2 1400 z -21 1 -1 z 1 2 -1 z 1 2 524288 -1 z 3 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["5", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], ",", FractionBox["5", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["1225", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "2048"], "-", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2205"]], "-", RowBox[List["1427334", " ", "z"]], "-", RowBox[List["10006664", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["24877360", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1070208", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], RowBox[List["1572864", " ", "z"]]], "-", FractionBox[RowBox[List["35", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "21"]], "+", RowBox[List["1400", " ", "z"]], "+", RowBox[List["33600", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["134400", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["169344", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["3072", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]]]], RowBox[List["524288", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "-", FractionBox[RowBox[List["3675", " ", 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"]]], "1024"], "+", RowBox[List[FractionBox["3675", "512"], " ", 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"]]]]], "]"]]]], "+", RowBox[List[FractionBox["3675", "512"], " ", 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"]]]]]]], "]"]]]], "-", RowBox[List[FractionBox["3675", "512"], " ", 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"]]]]]]], "]"]]]]]]]]]]

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

 2007-05-02