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.btjo.01

 Input Form

 Hypergeometric2F1[-(7/8), 3, 1/8, -z] == (1/1024) (7 (-((8 (31 + 23 z))/(1 + z)^2) + (345/7) (8 + 7 (-1)^(7/8) z^(7/8) Log[1 - (-1)^(1/8) z^(1/8)] - 7 (-1)^(7/8) z^(7/8) Log[1 + (-1)^(1/8) z^(1/8)] + 7 (-1)^(5/8) z^(7/8) Log[1 - (-1)^(3/8) z^(1/8)] - 7 (-1)^(5/8) z^(7/8) Log[1 + (-1)^(3/8) z^(1/8)] + 7 (-1)^(3/8) z^(7/8) Log[1 - (-1)^(5/8) z^(1/8)] - 7 (-1)^(3/8) z^(7/8) Log[1 + (-1)^(5/8) z^(1/8)] + 7 (-1)^(1/8) z^(7/8) Log[1 - (-1)^(7/8) z^(1/8)] - 7 (-1)^(1/8) z^(7/8) Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["7", "8"]]], ",", "3", ",", FractionBox["1", "8"], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "1024"], RowBox[List["(", RowBox[List["7", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["8", " ", RowBox[List["(", RowBox[List["31", "+", RowBox[List["23", " ", "z"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "2"]]]], "+", RowBox[List[FractionBox["345", "7"], " ", RowBox[List["(", RowBox[List["8", "+", RowBox[List["7", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["7", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["7", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["7", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List["7", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["7", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List["7", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["7", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List["7", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["7", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["7", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["7", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( - 7 8 , 3 ; 1 8 ; - 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["7", "8"]]], 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[TagBox[FractionBox["1", "8"], 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 1024 ( 7 ( 345 7 ( 7 ( - 1 ) 7 / 8 z 7 / 8 log ( 1 - - 1 8 z 8 ) - 7 ( - 1 ) 7 / 8 z 7 / 8 log ( - 1 8 z 8 + 1 ) + 7 ( - 1 ) 5 / 8 z 7 / 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 7 ( - 1 ) 5 / 8 z 7 / 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 7 ( - 1 ) 3 / 8 z 7 / 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 7 ( - 1 ) 3 / 8 z 7 / 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 7 - 1 8 z 7 / 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 7 - 1 8 z 7 / 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) + 8 ) - 8 ( 23 z + 31 ) ( z + 1 ) 2 ) ) HypergeometricPFQ -1 7 8 3 1 8 -1 z 1 1024 7 345 7 7 -1 7 8 z 7 8 1 -1 -1 1 8 z 1 8 -1 7 -1 7 8 z 7 8 -1 1 8 z 1 8 1 7 -1 5 8 z 7 8 1 -1 -1 3 8 z 1 8 -1 7 -1 5 8 z 7 8 -1 3 8 z 1 8 1 7 -1 3 8 z 7 8 1 -1 -1 5 8 z 1 8 -1 7 -1 3 8 z 7 8 -1 5 8 z 1 8 1 7 -1 1 8 z 7 8 1 -1 -1 7 8 z 1 8 -1 7 -1 1 8 z 7 8 -1 7 8 z 1 8 1 8 -1 8 23 z 31 z 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["7", "8"]]], ",", "3", ",", FractionBox["1", "8"], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["7", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["8", " ", RowBox[List["(", RowBox[List["31", "+", RowBox[List["23", " ", "z"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "2"]]]], "+", RowBox[List[FractionBox["345", "7"], " ", RowBox[List["(", RowBox[List["8", "+", RowBox[List["7", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["7", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["7", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["7", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List["7", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["7", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List["7", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["7", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List["7", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["7", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["7", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["7", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]]]], ")"]]]]]], ")"]]]], "1024"]]]]]

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

 2007-05-02