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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c9bv.01

 Input Form

 Hypergeometric2F1[3, 37/8, 45/8, -z] == (1/1024) (37 (-((8 (13 + 21 z))/(1 + z)^2) + 609 (-(8/(5 z^4)) + 8/(13 z^3) - 8/(21 z^2) + 8/(29 z) + (1/z^(37/8)) ((-1)^(1/8) ((-1)^(1/4) Log[1 - (-1)^(1/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(1/8) z^(1/8)] - Log[1 - (-1)^(3/8) z^(1/8)] + Log[1 + (-1)^(3/8) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(5/8) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(5/8) z^(1/8)] + I Log[1 - (-1)^(7/8) z^(1/8)] - I Log[1 + (-1)^(7/8) z^(1/8)])))))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["3", ",", FractionBox["37", "8"], ",", FractionBox["45", "8"], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "1024"], RowBox[List["(", RowBox[List["37", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["8", " ", RowBox[List["(", RowBox[List["13", "+", RowBox[List["21", " ", "z"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "2"]]]], "+", RowBox[List["609", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox["8", RowBox[List["5", " ", SuperscriptBox["z", "4"]]]]]], "+", FractionBox["8", RowBox[List["13", " ", SuperscriptBox["z", "3"]]]], "-", FractionBox["8", RowBox[List["21", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox["8", RowBox[List["29", " ", "z"]]], "+", RowBox[List[FractionBox["1", SuperscriptBox["z", RowBox[List["37", "/", "8"]]]], RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", 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[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", 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["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "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[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", 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[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", 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["\[ImaginaryI]", " ", 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["\[ImaginaryI]", " ", 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 ( 3 , 37 8 ; 45 8 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["37", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["45", "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 ( 37 ( 609 ( 1 z 37 / 8 ( - 1 8 ( - 1 4 log ( 1 - - 1 8 z 8 ) - - 1 4 log ( - 1 8 z 8 + 1 ) - log ( 1 - ( - 1 ) 3 / 8 z 8 ) + log ( ( - 1 ) 3 / 8 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + log ( 1 - ( - 1 ) 7 / 8 z 8 ) - log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) + 8 29 z - 8 21 z 2 + 8 13 z 3 - 8 5 z 4 ) - 8 ( 21 z + 13 ) ( z + 1 ) 2 ) ) HypergeometricPFQ 3 37 8 45 8 -1 z 1 1024 37 609 1 z 37 8 -1 -1 1 8 -1 1 4 1 -1 -1 1 8 z 1 8 -1 -1 1 4 -1 1 8 z 1 8 1 -1 1 -1 -1 3 8 z 1 8 -1 3 8 z 1 8 1 -1 -1 3 4 1 -1 -1 5 8 z 1 8 -1 3 4 -1 5 8 z 1 8 1 1 -1 -1 7 8 z 1 8 -1 -1 7 8 z 1 8 1 8 29 z -1 -1 8 21 z 2 -1 8 13 z 3 -1 -1 8 5 z 4 -1 -1 8 21 z 13 z 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["3", ",", FractionBox["37", "8"], ",", FractionBox["45", "8"], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["37", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["8", " ", RowBox[List["(", RowBox[List["13", "+", RowBox[List["21", " ", "z"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "2"]]]], "+", RowBox[List["609", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox["8", RowBox[List["5", " ", SuperscriptBox["z", "4"]]]]]], "+", FractionBox["8", RowBox[List["13", " ", SuperscriptBox["z", "3"]]]], "-", FractionBox["8", RowBox[List["21", " ", SuperscriptBox["z", "2"]]]], "+", FractionBox["8", RowBox[List["29", " ", "z"]]], "+", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", 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[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", 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["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "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[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", 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[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", 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["\[ImaginaryI]", " ", 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["\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["7", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]]]], ")"]]]], SuperscriptBox["z", RowBox[List["37", "/", "8"]]]]]], ")"]]]]]], ")"]]]], "1024"]]]]]

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

 2007-05-02