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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c2dy.01

 Input Form

 Hypergeometric2F1[9/8, 3, 41/8, -z] == -((1/(1048576 z^(33/8))) (4675 (-1)^(1/8) (30600 (-1)^(7/8) z^(1/8) + 29648 (-1)^(7/8) z^(9/8) + 72 (-1)^(7/8) z^(17/8) - 9 (-1)^(3/4) (-425 - 459 z - 27 z^2 + 7 z^3) Log[1 - (-1)^(1/8) z^(1/8)] + 9 (-1)^(3/4) (-425 - 459 z - 27 z^2 + 7 z^3) Log[1 + (-1)^(1/8) z^(1/8)] + 3825 I Log[1 - (-1)^(3/8) z^(1/8)] + 4131 I z Log[1 - (-1)^(3/8) z^(1/8)] + 243 I z^2 Log[1 - (-1)^(3/8) z^(1/8)] - 63 I z^3 Log[1 - (-1)^(3/8) z^(1/8)] - 3825 I Log[1 + (-1)^(3/8) z^(1/8)] - 4131 I z Log[1 + (-1)^(3/8) z^(1/8)] - 243 I z^2 Log[1 + (-1)^(3/8) z^(1/8)] + 63 I z^3 Log[1 + (-1)^(3/8) z^(1/8)] + 3825 (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] + 4131 (-1)^(1/4) z Log[1 - (-1)^(5/8) z^(1/8)] + 243 (-1)^(1/4) z^2 Log[1 - (-1)^(5/8) z^(1/8)] - 63 (-1)^(1/4) z^3 Log[1 - (-1)^(5/8) z^(1/8)] - 3825 (-1)^(1/4) Log[1 + (-1)^(5/8) z^(1/8)] - 4131 (-1)^(1/4) z Log[1 + (-1)^(5/8) z^(1/8)] - 243 (-1)^(1/4) z^2 Log[1 + (-1)^(5/8) z^(1/8)] + 63 (-1)^(1/4) z^3 Log[1 + (-1)^(5/8) z^(1/8)] + 3825 Log[1 - (-1)^(7/8) z^(1/8)] + 4131 z Log[1 - (-1)^(7/8) z^(1/8)] + 243 z^2 Log[1 - (-1)^(7/8) z^(1/8)] - 63 z^3 Log[1 - (-1)^(7/8) z^(1/8)] - 3825 Log[1 + (-1)^(7/8) z^(1/8)] - 4131 z Log[1 + (-1)^(7/8) z^(1/8)] - 243 z^2 Log[1 + (-1)^(7/8) z^(1/8)] + 63 z^3 Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

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 MathML Form

 2 F 1 ( 9 8 , 3 ; 41 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["9", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["41", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "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 z 33 / 8 ( 4675 - 1 8 ( - 63 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 3 + 63 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 3 - 63 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 3 + 63 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 3 - 63 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 3 + 63 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 3 + 72 ( - 1 ) 7 / 8 z 17 / 8 + 243 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 2 - 243 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 2 + 243 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 2 - 243 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 2 + 243 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 2 - 243 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 2 + 29648 ( - 1 ) 7 / 8 z 9 / 8 + 4131 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z - 4131 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z + 4131 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z - 4131 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z + 4131 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z - 4131 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z + 30600 ( - 1 ) 7 / 8 z 8 - 9 ( - 1 ) 3 / 4 ( 7 z 3 - 27 z 2 - 459 z - 425 ) log ( 1 - - 1 8 z 8 ) + 9 ( - 1 ) 3 / 4 ( 7 z 3 - 27 z 2 - 459 z - 425 ) log ( - 1 8 z 8 + 1 ) + 3825 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 3825 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 3825 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 3825 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 3825 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 3825 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) HypergeometricPFQ 9 8 3 41 8 -1 z -1 1 1048576 z 33 8 -1 4675 -1 1 8 -63 1 -1 -1 3 8 z 1 8 z 3 63 -1 3 8 z 1 8 1 z 3 -1 63 -1 1 4 1 -1 -1 5 8 z 1 8 z 3 63 -1 1 4 -1 5 8 z 1 8 1 z 3 -1 63 1 -1 -1 7 8 z 1 8 z 3 63 -1 7 8 z 1 8 1 z 3 72 -1 7 8 z 17 8 243 1 -1 -1 3 8 z 1 8 z 2 -1 243 -1 3 8 z 1 8 1 z 2 243 -1 1 4 1 -1 -1 5 8 z 1 8 z 2 -1 243 -1 1 4 -1 5 8 z 1 8 1 z 2 243 1 -1 -1 7 8 z 1 8 z 2 -1 243 -1 7 8 z 1 8 1 z 2 29648 -1 7 8 z 9 8 4131 1 -1 -1 3 8 z 1 8 z -1 4131 -1 3 8 z 1 8 1 z 4131 -1 1 4 1 -1 -1 5 8 z 1 8 z -1 4131 -1 1 4 -1 5 8 z 1 8 1 z 4131 1 -1 -1 7 8 z 1 8 z -1 4131 -1 7 8 z 1 8 1 z 30600 -1 7 8 z 1 8 -1 9 -1 3 4 7 z 3 -1 27 z 2 -1 459 z -425 1 -1 -1 1 8 z 1 8 9 -1 3 4 7 z 3 -1 27 z 2 -1 459 z -425 -1 1 8 z 1 8 1 3825 1 -1 -1 3 8 z 1 8 -1 3825 -1 3 8 z 1 8 1 3825 -1 1 4 1 -1 -1 5 8 z 1 8 -1 3825 -1 1 4 -1 5 8 z 1 8 1 3825 1 -1 -1 7 8 z 1 8 -1 3825 -1 7 8 z 1 8 1 [/itex]

 Rule Form

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

 2007-05-02