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.a87n.01

 Input Form

 HypergeometricPFQ[{-(5/2), -(5/2), 2}, {3/2, 7/2}, z] == (-135 + 1080 z + 141456 z^2 + 224320 z^3 + 36735 z^4)/(196608 z^2) + (5 (-9 + 75 z - 2500 z^2 - 4500 z^3 + 5325 z^4 + 1609 z^5) Log[1 - Sqrt[z]])/(131072 z^(5/2)) - (5 (-9 + 75 z - 2500 z^2 - 4500 z^3 + 5325 z^4 + 1609 z^5) Log[1 + Sqrt[z]])/(131072 z^(5/2)) - (75 (10 + 90 z + 75 z^2 + 7 z^3) PolyLog[2, -Sqrt[z]])/(16384 Sqrt[z]) + (75 (10 + 90 z + 75 z^2 + 7 z^3) PolyLog[2, Sqrt[z]])/(16384 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["5", "2"]]], ",", "2"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "135"]], "+", RowBox[List["1080", " ", "z"]], "+", RowBox[List["141456", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["224320", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["36735", " ", SuperscriptBox["z", "4"]]]]], RowBox[List["196608", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "9"]], "+", RowBox[List["75", " ", "z"]], "-", RowBox[List["2500", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["5325", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1609", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"]]], "]"]]]], RowBox[List["131072", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "9"]], "+", RowBox[List["75", " ", "z"]], "-", RowBox[List["2500", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["5325", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1609", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"]]], "]"]]]], RowBox[List["131072", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List["10", "+", RowBox[List["90", " ", "z"]], "+", RowBox[List["75", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SqrtBox["z"]]]]], "]"]]]], RowBox[List["16384", " ", SqrtBox["z"]]]], "+", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List["10", "+", RowBox[List["90", " ", "z"]], "+", RowBox[List["75", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SqrtBox["z"]]], "]"]]]], RowBox[List["16384", " ", SqrtBox["z"]]]]]]]]]]

 MathML Form

 3 F 2 ( - 5 2 , - 5 2 , 2 ; 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["5", "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["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] 36735 z 4 + 224320 z 3 + 141456 z 2 + 1080 z - 135 196608 z 2 + 5 ( 1609 z 5 + 5325 z 4 - 4500 z 3 - 2500 z 2 + 75 z - 9 ) log ( 1 - z ) 131072 z 5 / 2 - 5 ( 1609 z 5 + 5325 z 4 - 4500 z 3 - 2500 z 2 + 75 z - 9 ) log ( z + 1 ) 131072 z 5 / 2 - 75 ( 7 z 3 + 75 z 2 + 90 z + 10 ) Li PolyLog 2 ( - z ) 16384 z + 75 ( 7 z 3 + 75 z 2 + 90 z + 10 ) Li PolyLog 2 ( z ) 16384 z HypergeometricPFQ -1 5 2 -1 5 2 2 3 2 7 2 z 36735 z 4 224320 z 3 141456 z 2 1080 z -135 196608 z 2 -1 5 1609 z 5 5325 z 4 -1 4500 z 3 -1 2500 z 2 75 z -9 1 -1 z 1 2 131072 z 5 2 -1 -1 5 1609 z 5 5325 z 4 -1 4500 z 3 -1 2500 z 2 75 z -9 z 1 2 1 131072 z 5 2 -1 -1 75 7 z 3 75 z 2 90 z 10 PolyLog 2 -1 z 1 2 16384 z 1 2 -1 75 7 z 3 75 z 2 90 z 10 PolyLog 2 z 1 2 16384 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["5", "2"]]], ",", "2"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "135"]], "+", RowBox[List["1080", " ", "z"]], "+", RowBox[List["141456", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["224320", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["36735", " ", SuperscriptBox["z", "4"]]]]], RowBox[List["196608", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "9"]], "+", RowBox[List["75", " ", "z"]], "-", RowBox[List["2500", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["5325", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1609", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SqrtBox["z"]]], "]"]]]], RowBox[List["131072", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "9"]], "+", RowBox[List["75", " ", "z"]], "-", RowBox[List["2500", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4500", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["5325", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1609", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox["z"]]], "]"]]]], RowBox[List["131072", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List["10", "+", RowBox[List["90", " ", "z"]], "+", RowBox[List["75", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SqrtBox["z"]]]]], "]"]]]], RowBox[List["16384", " ", SqrtBox["z"]]]], "+", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List["10", "+", RowBox[List["90", " ", "z"]], "+", RowBox[List["75", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SqrtBox["z"]]], "]"]]]], RowBox[List["16384", " ", SqrtBox["z"]]]]]]]]]]

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

 2007-05-02