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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c5dy.01

 Input Form

 Hypergeometric2F1[15/8, 4, 31/8, z] == (1/65536) (115 (-((128 (-5 + z))/(-1 + z)^2) + (1/z^(23/8)) (120 z^(7/8) + 56 z^(15/8) + 105 Log[1 - z^(1/8)] + 105 I Log[1 - I z^(1/8)] - 105 I Log[1 + I z^(1/8)] - 105 Log[1 + z^(1/8)] + 105 (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] - 105 (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] + 105 (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] - 105 (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)]) + (1/z^(15/8)) (9 (8 z^(7/8) + 7 Log[1 - z^(1/8)] + 7 I Log[1 - I z^(1/8)] - 7 I Log[1 + I z^(1/8)] - 7 Log[1 + z^(1/8)] + 7 (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] - 7 (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] + 7 (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] - 7 (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( 15 8 , 4 ; 31 8 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["15", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["31", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["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 65536 ( 115 ( - 128 ( z - 5 ) ( z - 1 ) 2 + 1 z 23 / 8 ( 56 z 15 / 8 + 120 z 7 / 8 + 105 log ( 1 - z 8 ) + 105 log ( 1 - z 8 ) - 105 log ( z 8 + 1 ) - 105 log ( z 8 + 1 ) + 105 - 1 4 log ( 1 - - 1 4 z 8 ) - 105 - 1 4 log ( - 1 4 z 8 + 1 ) + 105 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 105 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) + 1 z 15 / 8 ( 9 ( 7 log ( 1 - z 8 ) + 7 log ( 1 - z 8 ) - 7 log ( z 8 + 1 ) - 7 log ( z 8 + 1 ) + 7 - 1 4 log ( 1 - - 1 4 z 8 ) - 7 - 1 4 log ( - 1 4 z 8 + 1 ) + 7 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 7 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 8 z 7 / 8 ) ) ) ) HypergeometricPFQ 15 8 4 31 8 z 1 65536 115 -1 128 z -5 z -1 2 -1 1 z 23 8 -1 56 z 15 8 120 z 7 8 105 1 -1 z 1 8 105 1 -1 z 1 8 -1 105 z 1 8 1 -1 105 z 1 8 1 105 -1 1 4 1 -1 -1 1 4 z 1 8 -1 105 -1 1 4 -1 1 4 z 1 8 1 105 -1 3 4 1 -1 -1 3 4 z 1 8 -1 105 -1 3 4 -1 3 4 z 1 8 1 1 z 15 8 -1 9 7 1 -1 z 1 8 7 1 -1 z 1 8 -1 7 z 1 8 1 -1 7 z 1 8 1 7 -1 1 4 1 -1 -1 1 4 z 1 8 -1 7 -1 1 4 -1 1 4 z 1 8 1 7 -1 3 4 1 -1 -1 3 4 z 1 8 -1 7 -1 3 4 -1 3 4 z 1 8 1 8 z 7 8 [/itex]

 Rule Form

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

 2007-05-02