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.b0e9.01

 Input Form

 Hypergeometric2F1[8/5, 4, 18/5, -z] == (1/9375) (52 ((25 (9 + 4 z))/(1 + z)^2 - (1/z^(8/5)) (14 (5 z^(3/5) - 3 Log[1 + z^(1/5)] - 3 (-1)^(2/5) Log[1 - (-1)^(1/5) z^(1/5)] - 3 (-1)^(4/5) Log[1 + (-1)^(2/5) z^(1/5)] + 3 (-1)^(1/5) Log[1 - (-1)^(3/5) z^(1/5)] + 3 (-1)^(3/5) Log[1 + (-1)^(4/5) z^(1/5)])) + (1/z^(13/5)) (80 z^(3/5) - 30 z^(8/5) - 48 Log[1 + z^(1/5)] - 48 (-1)^(2/5) Log[1 - (-1)^(1/5) z^(1/5)] - 48 (-1)^(4/5) Log[1 + (-1)^(2/5) z^(1/5)] + 48 (-1)^(1/5) Log[1 - (-1)^(3/5) z^(1/5)] + 48 (-1)^(3/5) Log[1 + (-1)^(4/5) z^(1/5)])))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["8", "5"], ",", "4", ",", FractionBox["18", "5"], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "9375"], RowBox[List["(", RowBox[List["52", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List["9", "+", RowBox[List["4", " ", "z"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "2"]], "-", RowBox[List[FractionBox["1", SuperscriptBox["z", RowBox[List["8", "/", "5"]]]], RowBox[List["(", RowBox[List["14", " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", SuperscriptBox["z", RowBox[List["3", "/", "5"]]]]], "-", RowBox[List["3", " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]]]], "-", RowBox[List["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "5"]]], " ", 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["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["4", "/", "5"]]], " ", 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["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", 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["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "5"]]], " ", 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[FractionBox["1", SuperscriptBox["z", RowBox[List["13", "/", "5"]]]], RowBox[List["(", RowBox[List[RowBox[List["80", " ", SuperscriptBox["z", RowBox[List["3", "/", "5"]]]]], "-", RowBox[List["30", " ", SuperscriptBox["z", RowBox[List["8", "/", "5"]]]]], "-", RowBox[List["48", " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]]]], "-", RowBox[List["48", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "5"]]], " ", 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["48", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["4", "/", "5"]]], " ", 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["48", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", 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["48", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "5"]]], " ", 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 ( 8 5 , 4 ; 18 5 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["8", "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["18", "5"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "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 9375 ( 52 ( 25 ( 4 z + 9 ) ( z + 1 ) 2 - 1 z 8 / 5 ( 14 ( - 3 log ( z 5 + 1 ) - 3 ( - 1 ) 2 / 5 log ( 1 - - 1 5 z 5 ) - 3 ( - 1 ) 4 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + 3 - 1 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + 3 ( - 1 ) 3 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) + 5 z 3 / 5 ) ) + 1 z 13 / 5 ( - 30 z 8 / 5 + 80 z 3 / 5 - 48 log ( z 5 + 1 ) - 48 ( - 1 ) 2 / 5 log ( 1 - - 1 5 z 5 ) - 48 ( - 1 ) 4 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + 48 - 1 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) + 48 ( - 1 ) 3 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) ) HypergeometricPFQ 8 5 4 18 5 -1 z 1 9375 52 25 4 z 9 z 1 2 -1 -1 1 z 8 5 -1 14 -3 z 1 5 1 -1 3 -1 2 5 1 -1 -1 1 5 z 1 5 -1 3 -1 4 5 -1 2 5 z 1 5 1 3 -1 1 5 1 -1 -1 3 5 z 1 5 3 -1 3 5 -1 4 5 z 1 5 1 5 z 3 5 1 z 13 5 -1 -30 z 8 5 80 z 3 5 -1 48 z 1 5 1 -1 48 -1 2 5 1 -1 -1 1 5 z 1 5 -1 48 -1 4 5 -1 2 5 z 1 5 1 48 -1 1 5 1 -1 -1 3 5 z 1 5 48 -1 3 5 -1 4 5 z 1 5 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["8", "5"], ",", "4", ",", FractionBox["18", "5"], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["52", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["25", " ", RowBox[List["(", RowBox[List["9", "+", RowBox[List["4", " ", "z"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "2"]], "-", FractionBox[RowBox[List["14", " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", SuperscriptBox["z", RowBox[List["3", "/", "5"]]]]], "-", RowBox[List["3", " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]]]], "-", RowBox[List["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "5"]]], " ", 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["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["4", "/", "5"]]], " ", 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["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", 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["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "5"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["4", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]]]], ")"]]]], SuperscriptBox["z", RowBox[List["8", "/", "5"]]]], "+", FractionBox[RowBox[List[RowBox[List["80", " ", SuperscriptBox["z", RowBox[List["3", "/", "5"]]]]], "-", RowBox[List["30", " ", SuperscriptBox["z", RowBox[List["8", "/", "5"]]]]], "-", RowBox[List["48", " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]], "]"]]]], "-", RowBox[List["48", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["2", "/", "5"]]], " ", 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["48", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["4", "/", "5"]]], " ", 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["48", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "5"]]], " ", 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["48", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "5"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["4", "/", "5"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "5"]]]]]]], "]"]]]]]], SuperscriptBox["z", RowBox[List["13", "/", "5"]]]]]], ")"]]]], "9375"]]]]]

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

 2007-05-02