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.a9n0.01

 Input Form

 HypergeometricPFQ[{-(5/2), -(1/2), 1/2}, {7/2, 7/2}, z] == (75 (Pi^2 + 20 Pi^2 z + 80 Pi^2 z^2))/(131072 (-z)^(5/2)) + (Sqrt[1 - z] (-4455 - 49270 z + 100976 z^2 + 1968 z^3 - 64 z^4))/ (262144 z^2) - (15 (-177 - 700 z + 800 z^2 - 3200 z^3) Log[Sqrt[1 - z] + Sqrt[-z]])/(262144 (-z)^(5/2)) - (225 (1 + 20 z + 80 z^2) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/ (65536 (-z)^(5/2)) + (225 (1 + 20 z + 80 z^2) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/(32768 (-z)^(5/2)) + (225 (1 + 20 z + 80 z^2) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/ (32768 (-z)^(5/2)) - (225 (1 + 20 z + 80 z^2) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/(32768 (-z)^(5/2))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], ",", RowBox[List["-", FractionBox["1", "2"]]], ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["7", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "2"], "+", RowBox[List["20", " ", SuperscriptBox["\[Pi]", "2"], " ", "z"]], "+", RowBox[List["80", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]], RowBox[List["131072", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4455"]], "-", RowBox[List["49270", " ", "z"]], "+", RowBox[List["100976", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1968", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["64", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], RowBox[List["262144", " ", SuperscriptBox["z", "2"]]]], "-", FractionBox[RowBox[List["15", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "177"]], "-", RowBox[List["700", " ", "z"]], "+", RowBox[List["800", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["3200", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]]]], RowBox[List["262144", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["225", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["20", " ", "z"]], "+", RowBox[List["80", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]], "2"]]], RowBox[List["65536", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List["225", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["20", " ", "z"]], "+", RowBox[List["80", " ", SuperscriptBox["z", "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["32768", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List["225", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["20", " ", "z"]], "+", RowBox[List["80", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List[RowBox[List["-", SqrtBox[RowBox[List["1", "-", "z"]]]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], RowBox[List["32768", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["225", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["20", " ", "z"]], "+", RowBox[List["80", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], RowBox[List["32768", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]]]]]]]]

 MathML Form

 3 F 2 ( - 5 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["5", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[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] - 225 ( 80 z 2 + 20 z + 1 ) log 2 ( 1 - z + - z ) 65536 ( - z ) 5 / 2 - 15 ( - 3200 z 3 + 800 z 2 - 700 z - 177 ) log ( 1 - z + - z ) 262144 ( - z ) 5 / 2 + 225 ( 80 z 2 + 20 z + 1 ) log ( 1 - z + - z + 1 ) log ( 1 - z + - z ) 32768 ( - z ) 5 / 2 + 75 ( 80 π 2 z 2 + 20 π 2 z + π 2 ) 131072 ( - z ) 5 / 2 + 1 - z ( - 64 z 4 + 1968 z 3 + 100976 z 2 - 49270 z - 4455 ) 262144 z 2 + 225 ( 80 z 2 + 20 z + 1 ) Li PolyLog 2 ( - 1 - z - - z ) 32768 ( - z ) 5 / 2 - 225 ( 80 z 2 + 20 z + 1 ) Li PolyLog 2 ( - 1 - z - - z + 1 ) 32768 ( - z ) 5 / 2 HypergeometricPFQ -1 5 2 -1 1 2 1 2 7 2 7 2 z -1 225 80 z 2 20 z 1 1 -1 z 1 2 -1 z 1 2 2 65536 -1 z 5 2 -1 -1 15 -3200 z 3 800 z 2 -1 700 z -177 1 -1 z 1 2 -1 z 1 2 262144 -1 z 5 2 -1 225 80 z 2 20 z 1 1 -1 z 1 2 -1 z 1 2 1 1 -1 z 1 2 -1 z 1 2 32768 -1 z 5 2 -1 75 80 2 z 2 20 2 z 2 131072 -1 z 5 2 -1 1 -1 z 1 2 -64 z 4 1968 z 3 100976 z 2 -1 49270 z -4455 262144 z 2 -1 225 80 z 2 20 z 1 PolyLog 2 -1 1 -1 z 1 2 -1 -1 z 1 2 32768 -1 z 5 2 -1 -1 225 80 z 2 20 z 1 PolyLog 2 -1 1 -1 z 1 2 -1 -1 z 1 2 1 32768 -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["5", "2"]]], ",", RowBox[List["-", FractionBox["1", "2"]]], ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["7", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "2"], "+", RowBox[List["20", " ", SuperscriptBox["\[Pi]", "2"], " ", "z"]], "+", RowBox[List["80", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]], RowBox[List["131072", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4455"]], "-", RowBox[List["49270", " ", "z"]], "+", RowBox[List["100976", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1968", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["64", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], RowBox[List["262144", " ", SuperscriptBox["z", "2"]]]], "-", FractionBox[RowBox[List["15", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "177"]], "-", RowBox[List["700", " ", "z"]], "+", RowBox[List["800", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["3200", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]]]], RowBox[List["262144", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["225", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["20", " ", "z"]], "+", RowBox[List["80", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "+", SqrtBox[RowBox[List["-", "z"]]]]], "]"]], "2"]]], RowBox[List["65536", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List["225", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["20", " ", "z"]], "+", RowBox[List["80", " ", SuperscriptBox["z", "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["32768", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List["225", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["20", " ", "z"]], "+", RowBox[List["80", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List[RowBox[List["-", SqrtBox[RowBox[List["1", "-", "z"]]]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], RowBox[List["32768", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["225", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["20", " ", "z"]], "+", RowBox[List["80", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]], "-", SqrtBox[RowBox[List["-", "z"]]]]]]], "]"]]]], RowBox[List["32768", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]]]]]]]]]

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

 2007-05-02