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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[4, 33/8, 41/8, -z] == (1/8192) (11 ((8 (209 + 234 z + 153 z^2))/(1 + z)^3 + (1/z^(33/8)) (30600 z^(1/8) - 3400 z^(9/8) + 1800 z^(17/8) - 1224 z^(25/8) - 3825 (-1)^(7/8) Log[1 - (-1)^(1/8) z^(1/8)] + 3825 (-1)^(7/8) Log[1 + (-1)^(1/8) z^(1/8)] - 3825 (-1)^(5/8) Log[1 - (-1)^(3/8) z^(1/8)] + 3825 (-1)^(5/8) Log[1 + (-1)^(3/8) z^(1/8)] - 3825 (-1)^(3/8) Log[1 - (-1)^(5/8) z^(1/8)] + 3825 (-1)^(3/8) Log[1 + (-1)^(5/8) z^(1/8)] - 3825 (-1)^(1/8) Log[1 - (-1)^(7/8) z^(1/8)] + 3825 (-1)^(1/8) Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["4", ",", FractionBox["33", "8"], ",", FractionBox["41", "8"], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "8192"], RowBox[List["(", RowBox[List["11", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["8", " ", RowBox[List["(", RowBox[List["209", "+", RowBox[List["234", " ", "z"]], "+", RowBox[List["153", " ", SuperscriptBox["z", "2"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "3"]], "+", RowBox[List[FractionBox["1", SuperscriptBox["z", RowBox[List["33", "/", "8"]]]], RowBox[List["(", RowBox[List[RowBox[List["30600", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]], "-", RowBox[List["3400", " ", SuperscriptBox["z", RowBox[List["9", "/", "8"]]]]], "+", RowBox[List["1800", " ", SuperscriptBox["z", RowBox[List["17", "/", "8"]]]]], "-", RowBox[List["1224", " ", SuperscriptBox["z", RowBox[List["25", "/", "8"]]]]], "-", RowBox[List["3825", " ", 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["1", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List["3825", " ", 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["1", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["3825", " ", 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["3", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List["3825", " ", 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["3", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["3825", " ", 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["5", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List["3825", " ", 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["5", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["3825", " ", 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["7", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List["3825", " ", 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["7", "/", "8"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 4 , 33 8 ; 41 8 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["33", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["41", "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 8192 ( 11 ( 8 ( 153 z 2 + 234 z + 209 ) ( z + 1 ) 3 + 1 z 33 / 8 ( - 1224 z 25 / 8 + 1800 z 17 / 8 - 3400 z 9 / 8 + 30600 z 8 - 3825 ( - 1 ) 7 / 8 log ( 1 - - 1 8 z 8 ) + 3825 ( - 1 ) 7 / 8 log ( - 1 8 z 8 + 1 ) - 3825 ( - 1 ) 5 / 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + 3825 ( - 1 ) 5 / 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - 3825 ( - 1 ) 3 / 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) + 3825 ( - 1 ) 3 / 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) - 3825 - 1 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) + 3825 - 1 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) ) HypergeometricPFQ 4 33 8 41 8 -1 z 1 8192 11 8 153 z 2 234 z 209 z 1 3 -1 1 z 33 8 -1 -1224 z 25 8 1800 z 17 8 -1 3400 z 9 8 30600 z 1 8 -1 3825 -1 7 8 1 -1 -1 1 8 z 1 8 3825 -1 7 8 -1 1 8 z 1 8 1 -1 3825 -1 5 8 1 -1 -1 3 8 z 1 8 3825 -1 5 8 -1 3 8 z 1 8 1 -1 3825 -1 3 8 1 -1 -1 5 8 z 1 8 3825 -1 3 8 -1 5 8 z 1 8 1 -1 3825 -1 1 8 1 -1 -1 7 8 z 1 8 3825 -1 1 8 -1 7 8 z 1 8 1 [/itex]

 Rule Form

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

 2007-05-02