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.a93v.01

 Input Form

 HypergeometricPFQ[{-(5/2), -(3/2), 2}, {7/2, 7/2}, z] == (7695 + 19215 z + 148001 z^2 + 53835 z^3 + 630 z^4)/(262144 z^2) + (15 (333 - 50 z - 4200 z^2 + 1800 z^3 + 2075 z^4 + 42 z^5) Log[1 - Sqrt[z]])/(524288 z^(5/2)) - (15 (333 - 50 z - 4200 z^2 + 1800 z^3 + 2075 z^4 + 42 z^5) Log[1 + Sqrt[z]])/(524288 z^(5/2)) - (225 (-3 - 20 z + 60 z^2 + 120 z^3 + 25 z^4) PolyLog[2, -Sqrt[z]])/ (131072 z^(5/2)) + (225 (-3 - 20 z + 60 z^2 + 120 z^3 + 25 z^4) PolyLog[2, Sqrt[z]])/(131072 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["3", "2"]]], ",", "2"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["7", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["7695", "+", RowBox[List["19215", " ", "z"]], "+", RowBox[List["148001", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["53835", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["630", " ", SuperscriptBox["z", "4"]]]]], RowBox[List["262144", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["15", " ", RowBox[List["(", RowBox[List["333", "-", RowBox[List["50", " ", "z"]], "-", RowBox[List["4200", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1800", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["2075", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["42", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"]]], "]"]]]], RowBox[List["524288", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["15", " ", RowBox[List["(", RowBox[List["333", "-", RowBox[List["50", " ", "z"]], "-", RowBox[List["4200", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1800", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["2075", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["42", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"]]], "]"]]]], RowBox[List["524288", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["225", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "-", RowBox[List["20", " ", "z"]], "+", RowBox[List["60", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["120", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["25", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SqrtBox["z"]]]]], "]"]]]], RowBox[List["131072", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List["225", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "-", RowBox[List["20", " ", "z"]], "+", RowBox[List["60", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["120", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["25", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SqrtBox["z"]]], "]"]]]], RowBox[List["131072", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]]]]]]]

 MathML Form

 3 F 2 ( - 5 2 , - 3 2 , 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["3", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["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] 630 z 4 + 53835 z 3 + 148001 z 2 + 19215 z + 7695 262144 z 2 + 15 ( 42 z 5 + 2075 z 4 + 1800 z 3 - 4200 z 2 - 50 z + 333 ) log ( 1 - z ) 524288 z 5 / 2 - 15 ( 42 z 5 + 2075 z 4 + 1800 z 3 - 4200 z 2 - 50 z + 333 ) log ( z + 1 ) 524288 z 5 / 2 - 225 ( 25 z 4 + 120 z 3 + 60 z 2 - 20 z - 3 ) Li PolyLog 2 ( - z ) 131072 z 5 / 2 + 225 ( 25 z 4 + 120 z 3 + 60 z 2 - 20 z - 3 ) Li PolyLog 2 ( z ) 131072 z 5 / 2 HypergeometricPFQ -1 5 2 -1 3 2 2 7 2 7 2 z 630 z 4 53835 z 3 148001 z 2 19215 z 7695 262144 z 2 -1 15 42 z 5 2075 z 4 1800 z 3 -1 4200 z 2 -1 50 z 333 1 -1 z 1 2 524288 z 5 2 -1 -1 15 42 z 5 2075 z 4 1800 z 3 -1 4200 z 2 -1 50 z 333 z 1 2 1 524288 z 5 2 -1 -1 225 25 z 4 120 z 3 60 z 2 -1 20 z -3 PolyLog 2 -1 z 1 2 131072 z 5 2 -1 225 25 z 4 120 z 3 60 z 2 -1 20 z -3 PolyLog 2 z 1 2 131072 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["3", "2"]]], ",", "2"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["7", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["7695", "+", RowBox[List["19215", " ", "z"]], "+", RowBox[List["148001", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["53835", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["630", " ", SuperscriptBox["z", "4"]]]]], RowBox[List["262144", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["15", " ", RowBox[List["(", RowBox[List["333", "-", RowBox[List["50", " ", "z"]], "-", RowBox[List["4200", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1800", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["2075", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["42", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"]]], "]"]]]], RowBox[List["524288", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["15", " ", RowBox[List["(", RowBox[List["333", "-", RowBox[List["50", " ", "z"]], "-", RowBox[List["4200", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1800", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["2075", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["42", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"]]], "]"]]]], RowBox[List["524288", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["225", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "-", RowBox[List["20", " ", "z"]], "+", RowBox[List["60", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["120", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["25", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SqrtBox["z"]]]]], "]"]]]], RowBox[List["131072", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "+", FractionBox[RowBox[List["225", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "-", RowBox[List["20", " ", "z"]], "+", RowBox[List["60", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["120", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["25", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SqrtBox["z"]]], "]"]]]], RowBox[List["131072", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]]]]]]]

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

 2007-05-02