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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[3/8, 5, 35/8, z] == (1/268435456) (5643 (-(8192/(-1 + z)) - (1/z^(3/8)) (13195 (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)])) - (1/z^(11/8)) (1365 (8 z^(3/8) + 3 Log[1 - z^(1/8)] + 3 I Log[1 - I z^(1/8)] - 3 I Log[1 + I z^(1/8)] - 3 Log[1 + z^(1/8)] - 3 (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] + 3 (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] - 3 (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] + 3 (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)])) - (1/z^(19/8)) (65 (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/(3 z^(27/8))) (5 (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)]))))

 Standard Form

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 MathML Form

 2 F 1 ( 3 8 , 5 ; 35 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["3", "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["35", "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 ( 5643 ( - 1 z 3 / 8 ( 13195 ( 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 ) ) ) - 1 z 11 / 8 ( 1365 ( 3 log ( 1 - z 8 ) + 3 log ( 1 - z 8 ) - 3 log ( z 8 + 1 ) - 3 log ( z 8 + 1 ) - 3 - 1 4 log ( 1 - - 1 4 z 8 ) + 3 - 1 4 log ( - 1 4 z 8 + 1 ) - 3 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 3 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 8 z 3 / 8 ) ) - 1 z 19 / 8 ( 65 ( 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 3 z 27 / 8 ( 5 ( 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 ) ) ) - 8192 z - 1 ) ) HypergeometricPFQ 3 8 5 35 8 z 1 268435456 5643 -1 1 z 3 8 -1 13195 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 1 z 11 8 -1 1365 3 1 -1 z 1 8 3 1 -1 z 1 8 -1 3 z 1 8 1 -1 3 z 1 8 1 -1 3 -1 1 4 1 -1 -1 1 4 z 1 8 3 -1 1 4 -1 1 4 z 1 8 1 -1 3 -1 3 4 1 -1 -1 3 4 z 1 8 3 -1 3 4 -1 3 4 z 1 8 1 8 z 3 8 -1 1 z 19 8 -1 65 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 3 z 27 8 -1 5 264 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 8192 z -1 -1 [/itex]

 Rule Form

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

 2007-05-02