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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c1pb.01

 Input Form

 Hypergeometric2F1[1, 21/8, 29/8, -z] == -((1/(520 z^(21/8))) (21 (-1)^(1/8) (-104 (-1)^(7/8) z^(5/8) + 40 (-1)^(7/8) z^(13/8) - 65 (-1)^(1/4) Log[1 - (-1)^(1/8) z^(1/8)] + 65 (-1)^(1/4) Log[1 + (-1)^(1/8) z^(1/8)] + 65 Log[1 - (-1)^(3/8) z^(1/8)] - 65 Log[1 + (-1)^(3/8) z^(1/8)] + 65 (-1)^(3/4) Log[1 - (-1)^(5/8) z^(1/8)] - 65 (-1)^(3/4) Log[1 + (-1)^(5/8) z^(1/8)] - 65 I Log[1 - (-1)^(7/8) z^(1/8)] + 65 I Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

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 MathML Form

 2 F 1 ( 1 , 21 8 ; 29 8 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["21", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["29", "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] - 1 520 z 21 / 8 ( 21 - 1 8 ( 40 ( - 1 ) 7 / 8 z 13 / 8 - 104 ( - 1 ) 7 / 8 z 5 / 8 - 65 - 1 4 log ( 1 - - 1 8 z 8 ) + 65 - 1 4 log ( - 1 8 z 8 + 1 ) + 65 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 65 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 65 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 65 ( - 1 ) 3 / 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) - 65 log ( 1 - ( - 1 ) 7 / 8 z 8 ) + 65 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) HypergeometricPFQ 1 21 8 29 8 -1 z -1 1 520 z 21 8 -1 21 -1 1 8 40 -1 7 8 z 13 8 -1 104 -1 7 8 z 5 8 -1 65 -1 1 4 1 -1 -1 1 8 z 1 8 65 -1 1 4 -1 1 8 z 1 8 1 65 1 -1 -1 3 8 z 1 8 -1 65 -1 3 8 z 1 8 1 65 -1 3 4 1 -1 -1 5 8 z 1 8 -1 65 -1 3 4 -1 5 8 z 1 8 1 -1 65 1 -1 -1 7 8 z 1 8 65 -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