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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c5wn.01

 Input Form

 Hypergeometric2F1[2, 31/8, 39/8, -z] == (31/64) (8/(1 + z) + (1/(105 z^(31/8))) (-2760 z^(7/8) + 1288 z^(15/8) - 840 z^(23/8) + 2415 (-1)^(1/8) Log[1 - (-1)^(1/8) z^(1/8)] - 2415 (-1)^(1/8) Log[1 + (-1)^(1/8) z^(1/8)] + 2415 (-1)^(3/8) Log[1 - (-1)^(3/8) z^(1/8)] - 2415 (-1)^(3/8) Log[1 + (-1)^(3/8) z^(1/8)] + 2415 (-1)^(5/8) Log[1 - (-1)^(5/8) z^(1/8)] - 2415 (-1)^(5/8) Log[1 + (-1)^(5/8) z^(1/8)] + 2415 (-1)^(7/8) Log[1 - (-1)^(7/8) z^(1/8)] - 2415 (-1)^(7/8) Log[1 + (-1)^(7/8) z^(1/8)]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["2", ",", FractionBox["31", "8"], ",", FractionBox["39", "8"], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["31", "64"], " ", RowBox[List["(", RowBox[List[FractionBox["8", RowBox[List["1", "+", "z"]]], "+", RowBox[List[FractionBox["1", RowBox[List["105", " ", SuperscriptBox["z", RowBox[List["31", "/", "8"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2760"]], " ", SuperscriptBox["z", RowBox[List["7", "/", "8"]]]]], "+", RowBox[List["1288", " ", SuperscriptBox["z", RowBox[List["15", "/", "8"]]]]], "-", RowBox[List["840", " ", SuperscriptBox["z", RowBox[List["23", "/", "8"]]]]], "+", RowBox[List["2415", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "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["2415", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "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["2415", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "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["2415", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "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["2415", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "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["2415", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "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["2415", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], 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["2415", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], 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 ( 2 , 31 8 ; 39 8 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["31", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["39", "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] 31 64 ( 1 105 z 31 / 8 ( - 840 z 23 / 8 + 1288 z 15 / 8 - 2760 z 7 / 8 + 2415 - 1 8 log ( 1 - - 1 8 z 8 ) - 2415 - 1 8 log ( - 1 8 z 8 + 1 ) + 2415 ( - 1 ) 3 / 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 2415 ( - 1 ) 3 / 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 2415 ( - 1 ) 5 / 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 2415 ( - 1 ) 5 / 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 2415 ( - 1 ) 7 / 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 2415 ( - 1 ) 7 / 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) + 8 z + 1 ) HypergeometricPFQ 2 31 8 39 8 -1 z 31 64 1 105 z 31 8 -1 -840 z 23 8 1288 z 15 8 -1 2760 z 7 8 2415 -1 1 8 1 -1 -1 1 8 z 1 8 -1 2415 -1 1 8 -1 1 8 z 1 8 1 2415 -1 3 8 1 -1 -1 3 8 z 1 8 -1 2415 -1 3 8 -1 3 8 z 1 8 1 2415 -1 5 8 1 -1 -1 5 8 z 1 8 -1 2415 -1 5 8 -1 5 8 z 1 8 1 2415 -1 7 8 1 -1 -1 7 8 z 1 8 -1 2415 -1 7 8 -1 7 8 z 1 8 1 8 z 1 -1 [/itex]

 Rule Form

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

 2007-05-02