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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(7/8), 2, 9/8, -z] == (1/(512 z^(1/8))) ((-1)^(1/8) (-120 (-1)^(7/8) z^(1/8) + 7 (-1)^(3/4) (7 + 15 z) Log[1 - (-1)^(1/8) z^(1/8)] - 7 (-1)^(3/4) (7 + 15 z) Log[1 + (-1)^(1/8) z^(1/8)] + 49 I Log[1 - (-1)^(3/8) z^(1/8)] + 105 I z Log[1 - (-1)^(3/8) z^(1/8)] - 49 I Log[1 + (-1)^(3/8) z^(1/8)] - 105 I z Log[1 + (-1)^(3/8) z^(1/8)] + 49 (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] + 105 (-1)^(1/4) z Log[1 - (-1)^(5/8) z^(1/8)] - 49 (-1)^(1/4) Log[1 + (-1)^(5/8) z^(1/8)] - 105 (-1)^(1/4) z Log[1 + (-1)^(5/8) z^(1/8)] + 49 Log[1 - (-1)^(7/8) z^(1/8)] + 105 z Log[1 - (-1)^(7/8) z^(1/8)] - 49 Log[1 + (-1)^(7/8) z^(1/8)] - 105 z Log[1 + (-1)^(7/8) z^(1/8)]))

 Standard Form

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 MathML Form

 2 F 1 ( - 7 8 , 2 ; 9 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["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["9", "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] 1 512 z 8 ( - 1 8 ( 7 ( - 1 ) 3 / 4 ( 15 z + 7 ) log ( 1 - - 1 8 z 8 ) - 7 ( - 1 ) 3 / 4 ( 15 z + 7 ) log ( - 1 8 z 8 + 1 ) + 105 z log ( 1 - ( - 1 ) 3 / 8 z 8 ) + 49 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 105 z log ( ( - 1 ) 3 / 8 z 8 + 1 ) - 49 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 105 - 1 4 z log ( 1 - ( - 1 ) 5 / 8 z 8 ) + 49 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 105 - 1 4 z log ( ( - 1 ) 5 / 8 z 8 + 1 ) - 49 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 105 z log ( 1 - ( - 1 ) 7 / 8 z 8 ) + 49 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 105 z log ( ( - 1 ) 7 / 8 z 8 + 1 ) - 49 log ( ( - 1 ) 7 / 8 z 8 + 1 ) - 120 ( - 1 ) 7 / 8 z 8 ) ) HypergeometricPFQ -1 7 8 2 9 8 -1 z 1 512 z 1 8 -1 -1 1 8 7 -1 3 4 15 z 7 1 -1 -1 1 8 z 1 8 -1 7 -1 3 4 15 z 7 -1 1 8 z 1 8 1 105 z 1 -1 -1 3 8 z 1 8 49 1 -1 -1 3 8 z 1 8 -1 105 z -1 3 8 z 1 8 1 -1 49 -1 3 8 z 1 8 1 105 -1 1 4 z 1 -1 -1 5 8 z 1 8 49 -1 1 4 1 -1 -1 5 8 z 1 8 -1 105 -1 1 4 z -1 5 8 z 1 8 1 -1 49 -1 1 4 -1 5 8 z 1 8 1 105 z 1 -1 -1 7 8 z 1 8 49 1 -1 -1 7 8 z 1 8 -1 105 z -1 7 8 z 1 8 1 -1 49 -1 7 8 z 1 8 1 -1 120 -1 7 8 z 1 8 [/itex]

 Rule Form

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

 2007-05-02