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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c4ol.01

 Input Form

 Hypergeometric2F1[13/8, 5, 29/8, z] == (1/2097152) (91 (-((64 (403 - 374 z + 99 z^2))/(-1 + z)^3) + (1/z^(21/8)) (33 (104 z^(5/8) + 40 z^(13/8) + 65 Log[1 - z^(1/8)] - 65 I Log[1 - I z^(1/8)] + 65 I Log[1 + I z^(1/8)] - 65 Log[1 + z^(1/8)] + 65 (-1)^(3/4) Log[1 - (-1)^(1/4) z^(1/8)] - 65 (-1)^(3/4) Log[1 + (-1)^(1/4) z^(1/8)] + 65 (-1)^(1/4) Log[1 - (-1)^(3/4) z^(1/8)] - 65 (-1)^(1/4) Log[1 + (-1)^(3/4) z^(1/8)])) + (1/z^(13/8)) (627 (8 z^(5/8) + 5 Log[1 - z^(1/8)] - 5 I Log[1 - I z^(1/8)] + 5 I Log[1 + I z^(1/8)] - 5 Log[1 + z^(1/8)] + 5 (-1)^(3/4) Log[1 - (-1)^(1/4) z^(1/8)] - 5 (-1)^(3/4) Log[1 + (-1)^(1/4) z^(1/8)] + 5 (-1)^(1/4) Log[1 - (-1)^(3/4) z^(1/8)] - 5 (-1)^(1/4) Log[1 + (-1)^(3/4) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( 13 8 , 5 ; 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[FractionBox["13", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["5", 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["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 2097152 ( 91 ( - 64 ( 99 z 2 - 374 z + 403 ) ( z - 1 ) 3 + 1 z 21 / 8 ( 33 ( 40 z 13 / 8 + 104 z 5 / 8 + 65 log ( 1 - z 8 ) - 65 log ( 1 - z 8 ) + 65 log ( z 8 + 1 ) - 65 log ( z 8 + 1 ) + 65 ( - 1 ) 3 / 4 log ( 1 - - 1 4 z 8 ) - 65 ( - 1 ) 3 / 4 log ( - 1 4 z 8 + 1 ) + 65 - 1 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 65 - 1 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) + 1 z 13 / 8 ( 627 ( 5 log ( 1 - z 8 ) - 5 log ( 1 - z 8 ) + 5 log ( z 8 + 1 ) - 5 log ( z 8 + 1 ) + 5 ( - 1 ) 3 / 4 log ( 1 - - 1 4 z 8 ) - 5 ( - 1 ) 3 / 4 log ( - 1 4 z 8 + 1 ) + 5 - 1 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 5 - 1 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 8 z 5 / 8 ) ) ) ) HypergeometricPFQ 13 8 5 29 8 z 1 2097152 91 -1 64 99 z 2 -1 374 z 403 z -1 3 -1 1 z 21 8 -1 33 40 z 13 8 104 z 5 8 65 1 -1 z 1 8 -1 65 1 -1 z 1 8 65 z 1 8 1 -1 65 z 1 8 1 65 -1 3 4 1 -1 -1 1 4 z 1 8 -1 65 -1 3 4 -1 1 4 z 1 8 1 65 -1 1 4 1 -1 -1 3 4 z 1 8 -1 65 -1 1 4 -1 3 4 z 1 8 1 1 z 13 8 -1 627 5 1 -1 z 1 8 -1 5 1 -1 z 1 8 5 z 1 8 1 -1 5 z 1 8 1 5 -1 3 4 1 -1 -1 1 4 z 1 8 -1 5 -1 3 4 -1 1 4 z 1 8 1 5 -1 1 4 1 -1 -1 3 4 z 1 8 -1 5 -1 1 4 -1 3 4 z 1 8 1 8 z 5 8 [/itex]

 Rule Form

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

 2007-05-02