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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.bqx2.01

 Input Form

 Hypergeometric2F1[-(13/8), 6, 11/8, z] == (1/268435456) (13 (-((2048 (3727 - 6882 z + 3219 z^2))/(-1 + z)^3) - (1/z^(3/8)) (1464645 (Log[1 - z^(1/8)] + I Log[1 - I z^(1/8)] - I Log[1 + I z^(1/8)] - Log[1 + z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)])) - 26363610 (-(8/5) + z^(5/8) (-Log[1 - z^(1/8)] - I Log[1 - I z^(1/8)] + I Log[1 + I z^(1/8)] + Log[1 + z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] + (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)])) + 53741205 ((-(8/65)) (5 + 13 z) + z^(13/8) (-Log[1 - z^(1/8)] - I Log[1 - I z^(1/8)] + I Log[1 + I z^(1/8)] + Log[1 + z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] + (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 13 8 , 6 ; 11 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["13", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["11", "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 268435456 ( 13 ( - 2048 ( 3219 z 2 - 6882 z + 3727 ) ( z - 1 ) 3 - 1 z 3 / 8 ( 1464645 ( log ( 1 - z 8 ) + log ( 1 - z 8 ) - log ( z 8 + 1 ) - log ( z 8 + 1 ) - - 1 4 log ( 1 - - 1 4 z 8 ) + - 1 4 log ( - 1 4 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) - 26363610 ( z 5 / 8 ( - log ( 1 - z 8 ) - log ( 1 - z 8 ) + log ( z 8 + 1 ) + log ( z 8 + 1 ) + - 1 4 log ( 1 - - 1 4 z 8 ) - - 1 4 log ( - 1 4 z 8 + 1 ) + ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) - 8 5 ) + 53741205 ( z 13 / 8 ( - log ( 1 - z 8 ) - log ( 1 - z 8 ) + log ( z 8 + 1 ) + log ( z 8 + 1 ) + - 1 4 log ( 1 - - 1 4 z 8 ) - - 1 4 log ( - 1 4 z 8 + 1 ) + ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) - 8 65 ( 13 z + 5 ) ) ) ) HypergeometricPFQ -1 13 8 6 11 8 z 1 268435456 13 -1 2048 3219 z 2 -1 6882 z 3727 z -1 3 -1 -1 1 z 3 8 -1 1464645 1 -1 z 1 8 1 -1 z 1 8 -1 z 1 8 1 -1 z 1 8 1 -1 -1 1 4 1 -1 -1 1 4 z 1 8 -1 1 4 -1 1 4 z 1 8 1 -1 -1 3 4 1 -1 -1 3 4 z 1 8 -1 3 4 -1 3 4 z 1 8 1 -1 26363610 z 5 8 -1 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 z 1 8 1 -1 1 4 1 -1 -1 1 4 z 1 8 -1 -1 1 4 -1 1 4 z 1 8 1 -1 3 4 1 -1 -1 3 4 z 1 8 -1 -1 3 4 -1 3 4 z 1 8 1 -1 8 5 53741205 z 13 8 -1 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 z 1 8 1 -1 1 4 1 -1 -1 1 4 z 1 8 -1 -1 1 4 -1 1 4 z 1 8 1 -1 3 4 1 -1 -1 3 4 z 1 8 -1 -1 3 4 -1 3 4 z 1 8 1 -1 8 65 13 z 5 [/itex]

 Rule Form

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

 2007-05-02