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.a99w.01

 Input Form

 HypergeometricPFQ[{-(5/2), -(3/2), 3}, {3/2, 7/2}, z] == (3 (15 + 105 z + 32027 z^2 + 41345 z^3 + 1260 z^4))/(131072 z^2) + (15 (3 + 20 z - 1620 z^2 - 2640 z^3 + 3985 z^4 + 252 z^5) Log[1 - Sqrt[z]])/ (262144 z^(5/2)) - (15 (3 + 20 z - 1620 z^2 - 2640 z^3 + 3985 z^4 + 252 z^5) Log[1 + Sqrt[z]])/(262144 z^(5/2)) - (225 (6 + 60 z + 35 z^2) PolyLog[2, -Sqrt[z]])/(32768 Sqrt[z]) + (225 (6 + 60 z + 35 z^2) PolyLog[2, Sqrt[z]])/(32768 Sqrt[z])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["5", "2"]]], ",", RowBox[List["-", FractionBox["3", "2"]]], ",", "3"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["3", " ", RowBox[List["(", RowBox[List["15", "+", RowBox[List["105", " ", "z"]], "+", RowBox[List["32027", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["41345", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1260", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], RowBox[List["131072", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["15", " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["20", " ", "z"]], "-", RowBox[List["1620", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2640", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3985", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["252", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"]]], "]"]]]], RowBox[List["262144", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["15", " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["20", " ", "z"]], "-", RowBox[List["1620", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2640", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3985", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["252", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"]]], "]"]]]], RowBox[List["262144", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["225", " ", RowBox[List["(", RowBox[List["6", "+", RowBox[List["60", " ", "z"]], "+", RowBox[List["35", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SqrtBox["z"]]]]], "]"]]]], RowBox[List["32768", " ", SqrtBox["z"]]]], "+", FractionBox[RowBox[List["225", " ", RowBox[List["(", RowBox[List["6", "+", RowBox[List["60", " ", "z"]], "+", RowBox[List["35", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SqrtBox["z"]]], "]"]]]], RowBox[List["32768", " ", SqrtBox["z"]]]]]]]]]]

 MathML Form

 3 F 2 ( - 5 2 , - 3 2 , 3 ; 3 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["3", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", 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["3", "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] 3 ( 1260 z 4 + 41345 z 3 + 32027 z 2 + 105 z + 15 ) 131072 z 2 + 15 ( 252 z 5 + 3985 z 4 - 2640 z 3 - 1620 z 2 + 20 z + 3 ) log ( 1 - z ) 262144 z 5 / 2 - 15 ( 252 z 5 + 3985 z 4 - 2640 z 3 - 1620 z 2 + 20 z + 3 ) log ( z + 1 ) 262144 z 5 / 2 - 225 ( 35 z 2 + 60 z + 6 ) Li PolyLog 2 ( - z ) 32768 z + 225 ( 35 z 2 + 60 z + 6 ) Li PolyLog 2 ( z ) 32768 z HypergeometricPFQ -1 5 2 -1 3 2 3 3 2 7 2 z 3 1260 z 4 41345 z 3 32027 z 2 105 z 15 131072 z 2 -1 15 252 z 5 3985 z 4 -1 2640 z 3 -1 1620 z 2 20 z 3 1 -1 z 1 2 262144 z 5 2 -1 -1 15 252 z 5 3985 z 4 -1 2640 z 3 -1 1620 z 2 20 z 3 z 1 2 1 262144 z 5 2 -1 -1 225 35 z 2 60 z 6 PolyLog 2 -1 z 1 2 32768 z 1 2 -1 225 35 z 2 60 z 6 PolyLog 2 z 1 2 32768 z 1 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["3", "2"]]], ",", "3"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["3", " ", RowBox[List["(", RowBox[List["15", "+", RowBox[List["105", " ", "z"]], "+", RowBox[List["32027", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["41345", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1260", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], RowBox[List["131072", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["15", " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["20", " ", "z"]], "-", RowBox[List["1620", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2640", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3985", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["252", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"]]], "]"]]]], RowBox[List["262144", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["15", " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["20", " ", "z"]], "-", RowBox[List["1620", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2640", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3985", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["252", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"]]], "]"]]]], RowBox[List["262144", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["225", " ", RowBox[List["(", RowBox[List["6", "+", RowBox[List["60", " ", "z"]], "+", RowBox[List["35", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SqrtBox["z"]]]]], "]"]]]], RowBox[List["32768", " ", SqrtBox["z"]]]], "+", FractionBox[RowBox[List["225", " ", RowBox[List["(", RowBox[List["6", "+", RowBox[List["60", " ", "z"]], "+", RowBox[List["35", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SqrtBox["z"]]], "]"]]]], RowBox[List["32768", " ", SqrtBox["z"]]]]]]]]]]

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

 2007-05-02