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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(7/8), 4, 17/8, -z] == -((1/(1048576 z^(9/8) (1 + z))) (3 (-1)^(1/8) (5880 (-1)^(7/8) z^(1/8) + 84272 (-1)^(7/8) z^(9/8) + 85560 (-1)^(7/8) z^(17/8) - 105 (-1)^(3/4) (-7 + 315 z + 1035 z^2 + 713 z^3) Log[1 - (-1)^(1/8) z^(1/8)] + 105 (-1)^(3/4) (-7 + 315 z + 1035 z^2 + 713 z^3) Log[1 + (-1)^(1/8) z^(1/8)] + 735 I Log[1 - (-1)^(3/8) z^(1/8)] - 33075 I z Log[1 - (-1)^(3/8) z^(1/8)] - 108675 I z^2 Log[1 - (-1)^(3/8) z^(1/8)] - 74865 I z^3 Log[1 - (-1)^(3/8) z^(1/8)] - 735 I Log[1 + (-1)^(3/8) z^(1/8)] + 33075 I z Log[1 + (-1)^(3/8) z^(1/8)] + 108675 I z^2 Log[1 + (-1)^(3/8) z^(1/8)] + 74865 I z^3 Log[1 + (-1)^(3/8) z^(1/8)] + 735 (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] - 33075 (-1)^(1/4) z Log[1 - (-1)^(5/8) z^(1/8)] - 108675 (-1)^(1/4) z^2 Log[1 - (-1)^(5/8) z^(1/8)] - 74865 (-1)^(1/4) z^3 Log[1 - (-1)^(5/8) z^(1/8)] - 735 (-1)^(1/4) Log[1 + (-1)^(5/8) z^(1/8)] + 33075 (-1)^(1/4) z Log[1 + (-1)^(5/8) z^(1/8)] + 108675 (-1)^(1/4) z^2 Log[1 + (-1)^(5/8) z^(1/8)] + 74865 (-1)^(1/4) z^3 Log[1 + (-1)^(5/8) z^(1/8)] + 735 Log[1 - (-1)^(7/8) z^(1/8)] - 33075 z Log[1 - (-1)^(7/8) z^(1/8)] - 108675 z^2 Log[1 - (-1)^(7/8) z^(1/8)] - 74865 z^3 Log[1 - (-1)^(7/8) z^(1/8)] - 735 Log[1 + (-1)^(7/8) z^(1/8)] + 33075 z Log[1 + (-1)^(7/8) z^(1/8)] + 108675 z^2 Log[1 + (-1)^(7/8) z^(1/8)] + 74865 z^3 Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

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 MathML Form

 2 F 1 ( - 7 8 , 4 ; 17 8 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["7", "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["17", "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 1048576 z 9 / 8 ( z + 1 ) ( 3 - 1 8 ( - 74865 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 3 + 74865 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 3 - 74865 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 3 + 74865 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 3 - 74865 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 3 + 74865 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 3 + 85560 ( - 1 ) 7 / 8 z 17 / 8 - 108675 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 2 + 108675 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 2 - 108675 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 2 + 108675 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 2 - 108675 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 2 + 108675 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 2 + 84272 ( - 1 ) 7 / 8 z 9 / 8 - 33075 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z + 33075 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z - 33075 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z + 33075 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z - 33075 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z + 33075 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z + 5880 ( - 1 ) 7 / 8 z 8 - 105 ( - 1 ) 3 / 4 ( 713 z 3 + 1035 z 2 + 315 z - 7 ) log ( 1 - - 1 8 z 8 ) + 105 ( - 1 ) 3 / 4 ( 713 z 3 + 1035 z 2 + 315 z - 7 ) log ( - 1 8 z 8 + 1 ) + 735 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 735 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 735 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 735 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 735 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 735 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) HypergeometricPFQ -1 7 8 4 17 8 -1 z -1 1 1048576 z 9 8 z 1 -1 3 -1 1 8 -74865 1 -1 -1 3 8 z 1 8 z 3 74865 -1 3 8 z 1 8 1 z 3 -1 74865 -1 1 4 1 -1 -1 5 8 z 1 8 z 3 74865 -1 1 4 -1 5 8 z 1 8 1 z 3 -1 74865 1 -1 -1 7 8 z 1 8 z 3 74865 -1 7 8 z 1 8 1 z 3 85560 -1 7 8 z 17 8 -1 108675 1 -1 -1 3 8 z 1 8 z 2 108675 -1 3 8 z 1 8 1 z 2 -1 108675 -1 1 4 1 -1 -1 5 8 z 1 8 z 2 108675 -1 1 4 -1 5 8 z 1 8 1 z 2 -1 108675 1 -1 -1 7 8 z 1 8 z 2 108675 -1 7 8 z 1 8 1 z 2 84272 -1 7 8 z 9 8 -1 33075 1 -1 -1 3 8 z 1 8 z 33075 -1 3 8 z 1 8 1 z -1 33075 -1 1 4 1 -1 -1 5 8 z 1 8 z 33075 -1 1 4 -1 5 8 z 1 8 1 z -1 33075 1 -1 -1 7 8 z 1 8 z 33075 -1 7 8 z 1 8 1 z 5880 -1 7 8 z 1 8 -1 105 -1 3 4 713 z 3 1035 z 2 315 z -7 1 -1 -1 1 8 z 1 8 105 -1 3 4 713 z 3 1035 z 2 315 z -7 -1 1 8 z 1 8 1 735 1 -1 -1 3 8 z 1 8 -1 735 -1 3 8 z 1 8 1 735 -1 1 4 1 -1 -1 5 8 z 1 8 -1 735 -1 1 4 -1 5 8 z 1 8 1 735 1 -1 -1 7 8 z 1 8 -1 735 -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