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; }

 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.axfk.01

 Input Form

 Hypergeometric2F1[-(1/5), 4, 29/5, z] == -((1/(9765625 z^(24/5))) (798 (-1)^(1/5) (12 (-1)^(4/5) (-1 + z)^2 (399 + 378 z + 297 z^2 + 176 z^3) Log[1 - z^(1/5)] + 12 (-1 + z)^2 (399 + 378 z + 297 z^2 + 176 z^3) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(1/5) (-12 (-1 + z)^2 (399 + 378 z + 297 z^2 + 176 z^3) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (12 (-1 + z)^2 (399 + 378 z + 297 z^2 + 176 z^3) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (1197 - 728 z - 398 z^2 - 308 z^3 + 2112 z^4) - 12 (-1 + z)^2 (399 + 378 z + 297 z^2 + 176 z^3) Log[1 - (-1)^(4/5) z^(1/5)]))))))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["1", "5"]]], ",", "4", ",", FractionBox["29", "5"], ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List["9765625", " ", SuperscriptBox["z", RowBox[List["24", "/", "5"]]]]]], RowBox[List["(", RowBox[List["798", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["12", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["4", "/", "5"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["399", "+", RowBox[List["378", " ", "z"]], "+", RowBox[List["297", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["176", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]]]], "+", RowBox[List["12", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["399", "+", RowBox[List["378", " ", "z"]], "+", RowBox[List["297", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["176", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "12"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["399", "+", RowBox[List["378", " ", "z"]], "+", RowBox[List["297", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["176", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["12", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["399", "+", RowBox[List["378", " ", "z"]], "+", RowBox[List["297", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["176", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["4", "/", "5"]]], " ", RowBox[List["(", RowBox[List["1197", "-", RowBox[List["728", " ", "z"]], "-", RowBox[List["398", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["308", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["2112", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], "-", RowBox[List["12", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["399", "+", RowBox[List["378", " ", "z"]], "+", RowBox[List["297", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["176", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["4", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]]]]

 MathML Form

 2 F 1 ( - 1 5 , 4 ; 29 5 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["1", "5"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["29", "5"], 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] - 1 9765625 z 24 / 5 ( 798 - 1 5 ( 12 ( - 1 ) 4 / 5 ( 176 z 3 + 297 z 2 + 378 z + 399 ) log ( 1 - z 5 ) ( z - 1 ) 2 + 12 ( 176 z 3 + 297 z 2 + 378 z + 399 ) log ( - 1 5 z 5 + 1 ) ( z - 1 ) 2 + - 1 5 ( - 1 5 ( 12 ( 176 z 3 + 297 z 2 + 378 z + 399 ) log ( ( - 1 ) 3 / 5 z 5 + 1 ) ( z - 1 ) 2 + - 1 5 ( 5 - 1 5 z 4 / 5 ( 2112 z 4 - 308 z 3 - 398 z 2 - 728 z + 1197 ) - 12 ( z - 1 ) 2 ( 176 z 3 + 297 z 2 + 378 z + 399 ) log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) - 12 ( z - 1 ) 2 ( 176 z 3 + 297 z 2 + 378 z + 399 ) log ( 1 - ( - 1 ) 2 / 5 z 5 ) ) ) ) HypergeometricPFQ -1 1 5 4 29 5 z -1 1 9765625 z 24 5 -1 798 -1 1 5 12 -1 4 5 176 z 3 297 z 2 378 z 399 1 -1 z 1 5 z -1 2 12 176 z 3 297 z 2 378 z 399 -1 1 5 z 1 5 1 z -1 2 -1 1 5 -1 1 5 12 176 z 3 297 z 2 378 z 399 -1 3 5 z 1 5 1 z -1 2 -1 1 5 5 -1 1 5 z 4 5 2112 z 4 -1 308 z 3 -1 398 z 2 -1 728 z 1197 -1 12 z -1 2 176 z 3 297 z 2 378 z 399 1 -1 -1 4 5 z 1 5 -1 12 z -1 2 176 z 3 297 z 2 378 z 399 1 -1 -1 2 5 z 1 5 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["1", "5"]]], ",", "4", ",", FractionBox["29", "5"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["798", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["12", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["4", "/", "5"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["399", "+", RowBox[List["378", " ", "z"]], "+", RowBox[List["297", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["176", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]]]], "+", RowBox[List["12", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["399", "+", RowBox[List["378", " ", "z"]], "+", RowBox[List["297", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["176", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "12"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["399", "+", RowBox[List["378", " ", "z"]], "+", RowBox[List["297", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["176", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["12", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["399", "+", RowBox[List["378", " ", "z"]], "+", RowBox[List["297", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["176", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["4", "/", "5"]]], " ", RowBox[List["(", RowBox[List["1197", "-", RowBox[List["728", " ", "z"]], "-", RowBox[List["398", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["308", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["2112", " ", SuperscriptBox["z", "4"]]]]], ")"]]]], "-", RowBox[List["12", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["399", "+", RowBox[List["378", " ", "z"]], "+", RowBox[List["297", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["176", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["4", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], RowBox[List["9765625", " ", SuperscriptBox["z", RowBox[List["24", "/", "5"]]]]]]]]]]]]

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

 2007-05-02