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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c1kh.01

 Input Form

 Hypergeometric2F1[1, 9/8, 41/8, -z] == -((1/(8192 z^(33/8))) (11 (-1)^(1/8) (30600 (-1)^(7/8) z^(1/8) + 88400 (-1)^(7/8) z^(9/8) + 83400 (-1)^(7/8) z^(17/8) + 24576 (-1)^(7/8) z^(25/8) + 3825 (-1)^(3/4) (1 + z)^3 Log[1 - (-1)^(1/8) z^(1/8)] - 3825 (-1)^(3/4) (1 + z)^3 Log[1 + (-1)^(1/8) z^(1/8)] + 3825 I Log[1 - (-1)^(3/8) z^(1/8)] + 11475 I z Log[1 - (-1)^(3/8) z^(1/8)] + 11475 I z^2 Log[1 - (-1)^(3/8) z^(1/8)] + 3825 I z^3 Log[1 - (-1)^(3/8) z^(1/8)] - 3825 I Log[1 + (-1)^(3/8) z^(1/8)] - 11475 I z Log[1 + (-1)^(3/8) z^(1/8)] - 11475 I z^2 Log[1 + (-1)^(3/8) z^(1/8)] - 3825 I z^3 Log[1 + (-1)^(3/8) z^(1/8)] + 3825 (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] + 11475 (-1)^(1/4) z Log[1 - (-1)^(5/8) z^(1/8)] + 11475 (-1)^(1/4) z^2 Log[1 - (-1)^(5/8) z^(1/8)] + 3825 (-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)] - 11475 (-1)^(1/4) z Log[1 + (-1)^(5/8) z^(1/8)] - 11475 (-1)^(1/4) z^2 Log[1 + (-1)^(5/8) z^(1/8)] - 3825 (-1)^(1/4) z^3 Log[1 + (-1)^(5/8) z^(1/8)] + 3825 Log[1 - (-1)^(7/8) z^(1/8)] + 11475 z Log[1 - (-1)^(7/8) z^(1/8)] + 11475 z^2 Log[1 - (-1)^(7/8) z^(1/8)] + 3825 z^3 Log[1 - (-1)^(7/8) z^(1/8)] - 3825 Log[1 + (-1)^(7/8) z^(1/8)] - 11475 z Log[1 + (-1)^(7/8) z^(1/8)] - 11475 z^2 Log[1 + (-1)^(7/8) z^(1/8)] - 3825 z^3 Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

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 MathML Form

 2 F 1 ( 1 , 9 8 ; 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["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "8"], 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 8192 z 33 / 8 ( 11 - 1 8 ( 24576 ( - 1 ) 7 / 8 z 25 / 8 + 3825 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 3 - 3825 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 3 + 3825 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 3 - 3825 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 3 + 3825 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 3 - 3825 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 3 + 83400 ( - 1 ) 7 / 8 z 17 / 8 + 11475 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 2 - 11475 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 2 + 11475 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 2 - 11475 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 2 + 11475 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 2 - 11475 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 2 + 88400 ( - 1 ) 7 / 8 z 9 / 8 + 11475 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z - 11475 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z + 11475 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z - 11475 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z + 11475 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z - 11475 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z + 30600 ( - 1 ) 7 / 8 z 8 + 3825 ( - 1 ) 3 / 4 ( z + 1 ) 3 log ( 1 - - 1 8 z 8 ) - 3825 ( - 1 ) 3 / 4 ( z + 1 ) 3 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 1 9 8 41 8 -1 z -1 1 8192 z 33 8 -1 11 -1 1 8 24576 -1 7 8 z 25 8 3825 1 -1 -1 3 8 z 1 8 z 3 -1 3825 -1 3 8 z 1 8 1 z 3 3825 -1 1 4 1 -1 -1 5 8 z 1 8 z 3 -1 3825 -1 1 4 -1 5 8 z 1 8 1 z 3 3825 1 -1 -1 7 8 z 1 8 z 3 -1 3825 -1 7 8 z 1 8 1 z 3 83400 -1 7 8 z 17 8 11475 1 -1 -1 3 8 z 1 8 z 2 -1 11475 -1 3 8 z 1 8 1 z 2 11475 -1 1 4 1 -1 -1 5 8 z 1 8 z 2 -1 11475 -1 1 4 -1 5 8 z 1 8 1 z 2 11475 1 -1 -1 7 8 z 1 8 z 2 -1 11475 -1 7 8 z 1 8 1 z 2 88400 -1 7 8 z 9 8 11475 1 -1 -1 3 8 z 1 8 z -1 11475 -1 3 8 z 1 8 1 z 11475 -1 1 4 1 -1 -1 5 8 z 1 8 z -1 11475 -1 1 4 -1 5 8 z 1 8 1 z 11475 1 -1 -1 7 8 z 1 8 z -1 11475 -1 7 8 z 1 8 1 z 30600 -1 7 8 z 1 8 3825 -1 3 4 z 1 3 1 -1 -1 1 8 z 1 8 -1 3825 -1 3 4 z 1 3 -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