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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c1t8.01

 Input Form

 Hypergeometric2F1[1, 29/8, 45/8, z] == (1/(87360 z^(37/8))) (37 (-1)^(1/4) (-63336 (-1)^(3/4) z^(5/8) + 38976 (-1)^(3/4) z^(13/8) + 9280 (-1)^(3/4) z^(21/8) + 4160 (-1)^(3/4) z^(29/8) + 39585 (-1)^(3/4) (-1 + z) Log[1 - z^(1/8)] + 39585 (-1)^(1/4) (-1 + z) Log[1 - I z^(1/8)] + 39585 (-1)^(1/4) Log[1 + I z^(1/8)] - 39585 (-1)^(1/4) z Log[1 + I z^(1/8)] + 39585 (-1)^(3/4) Log[1 + z^(1/8)] - 39585 (-1)^(3/4) z Log[1 + z^(1/8)] + 39585 I Log[1 - (-1)^(1/4) z^(1/8)] - 39585 I z Log[1 - (-1)^(1/4) z^(1/8)] - 39585 I Log[1 + (-1)^(1/4) z^(1/8)] + 39585 I z Log[1 + (-1)^(1/4) z^(1/8)] + 39585 Log[1 - (-1)^(3/4) z^(1/8)] - 39585 z Log[1 - (-1)^(3/4) z^(1/8)] - 39585 Log[1 + (-1)^(3/4) z^(1/8)] + 39585 z Log[1 + (-1)^(3/4) z^(1/8)]))

 Standard Form

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 MathML Form

 2 F 1 ( 1 , 29 8 ; 45 8 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["29", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["45", "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 87360 z 37 / 8 ( 37 - 1 4 ( 4160 ( - 1 ) 3 / 4 z 29 / 8 + 9280 ( - 1 ) 3 / 4 z 21 / 8 + 38976 ( - 1 ) 3 / 4 z 13 / 8 - 39585 - 1 4 log ( z 8 + 1 ) z - 39585 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z - 39585 log ( 1 - - 1 4 z 8 ) z + 39585 log ( - 1 4 z 8 + 1 ) z - 39585 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z + 39585 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z - 63336 ( - 1 ) 3 / 4 z 5 / 8 + 39585 ( - 1 ) 3 / 4 ( z - 1 ) log ( 1 - z 8 ) + 39585 - 1 4 ( z - 1 ) log ( 1 - z 8 ) + 39585 - 1 4 log ( z 8 + 1 ) + 39585 ( - 1 ) 3 / 4 log ( z 8 + 1 ) + 39585 log ( 1 - - 1 4 z 8 ) - 39585 log ( - 1 4 z 8 + 1 ) + 39585 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 39585 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) HypergeometricPFQ 1 29 8 45 8 z 1 87360 z 37 8 -1 37 -1 1 4 4160 -1 3 4 z 29 8 9280 -1 3 4 z 21 8 38976 -1 3 4 z 13 8 -1 39585 -1 1 4 z 1 8 1 z -1 39585 -1 3 4 z 1 8 1 z -1 39585 1 -1 -1 1 4 z 1 8 z 39585 -1 1 4 z 1 8 1 z -1 39585 1 -1 -1 3 4 z 1 8 z 39585 -1 3 4 z 1 8 1 z -1 63336 -1 3 4 z 5 8 39585 -1 3 4 z -1 1 -1 z 1 8 39585 -1 1 4 z -1 1 -1 z 1 8 39585 -1 1 4 z 1 8 1 39585 -1 3 4 z 1 8 1 39585 1 -1 -1 1 4 z 1 8 -1 39585 -1 1 4 z 1 8 1 39585 1 -1 -1 3 4 z 1 8 -1 39585 -1 3 4 z 1 8 1 [/itex]

 Rule Form

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

 2007-05-02