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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c7d3.01

 Input Form

 Hypergeometric2F1[19/8, 4, 43/8, z] == (1/1048576) (5985 (-(1024/(-1 + z)) - (1/z^(19/8)) (5 (88 z^(3/8) + 24 z^(11/8) + 33 Log[1 - z^(1/8)] + 33 I Log[1 - I z^(1/8)] - 33 I Log[1 + I z^(1/8)] - 33 Log[1 + z^(1/8)] - 33 (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] + 33 (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] - 33 (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] + 33 (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)])) - (1/z^(27/8)) (2 (1672 z^(3/8) + 456 z^(11/8) + 264 z^(19/8) + 627 Log[1 - z^(1/8)] + 627 I Log[1 - I z^(1/8)] - 627 I Log[1 + I z^(1/8)] - 627 Log[1 + z^(1/8)] - 627 (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] + 627 (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] - 627 (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] + 627 (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)])) - 5643 (-((8 (1881 + 513 z + 297 z^2 + 209 z^3))/(5643 z^4)) + (1/z^(35/8)) (-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 ( 19 8 , 4 ; 43 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["19", "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["43", "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 1048576 ( 5985 ( - 1 z 19 / 8 ( 5 ( 24 z 11 / 8 + 88 z 3 / 8 + 33 log ( 1 - z 8 ) + 33 log ( 1 - z 8 ) - 33 log ( z 8 + 1 ) - 33 log ( z 8 + 1 ) - 33 - 1 4 log ( 1 - - 1 4 z 8 ) + 33 - 1 4 log ( - 1 4 z 8 + 1 ) - 33 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 33 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) - 1 z 27 / 8 ( 2 ( 264 z 19 / 8 + 456 z 11 / 8 + 1672 z 3 / 8 + 627 log ( 1 - z 8 ) + 627 log ( 1 - z 8 ) - 627 log ( z 8 + 1 ) - 627 log ( z 8 + 1 ) - 627 - 1 4 log ( 1 - - 1 4 z 8 ) + 627 - 1 4 log ( - 1 4 z 8 + 1 ) - 627 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 627 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) - 5643 ( 1 z 35 / 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 ( 209 z 3 + 297 z 2 + 513 z + 1881 ) 5643 z 4 ) - 1024 z - 1 ) ) HypergeometricPFQ 19 8 4 43 8 z 1 1048576 5985 -1 1 z 19 8 -1 5 24 z 11 8 88 z 3 8 33 1 -1 z 1 8 33 1 -1 z 1 8 -1 33 z 1 8 1 -1 33 z 1 8 1 -1 33 -1 1 4 1 -1 -1 1 4 z 1 8 33 -1 1 4 -1 1 4 z 1 8 1 -1 33 -1 3 4 1 -1 -1 3 4 z 1 8 33 -1 3 4 -1 3 4 z 1 8 1 -1 1 z 27 8 -1 2 264 z 19 8 456 z 11 8 1672 z 3 8 627 1 -1 z 1 8 627 1 -1 z 1 8 -1 627 z 1 8 1 -1 627 z 1 8 1 -1 627 -1 1 4 1 -1 -1 1 4 z 1 8 627 -1 1 4 -1 1 4 z 1 8 1 -1 627 -1 3 4 1 -1 -1 3 4 z 1 8 627 -1 3 4 -1 3 4 z 1 8 1 -1 5643 1 z 35 8 -1 -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 8 209 z 3 297 z 2 513 z 1881 5643 z 4 -1 -1 1024 z -1 -1 [/itex]

 Rule Form

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

 2007-05-02