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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1/8, 2, 33/8, -z] == -((1/(196608 z^(25/8))) (425 (-1)^(1/8) (1224 (-1)^(7/8) z^(1/8) + 1808 (-1)^(7/8) z^(9/8) + 72 (-1)^(7/8) z^(17/8) - 9 (-1)^(3/4) (1 + z)^2 (-17 + 7 z) Log[1 - (-1)^(1/8) z^(1/8)] + 9 (-1)^(3/4) (1 + z)^2 (-17 + 7 z) Log[1 + (-1)^(1/8) z^(1/8)] + 153 I Log[1 - (-1)^(3/8) z^(1/8)] + 243 I z Log[1 - (-1)^(3/8) z^(1/8)] + 27 I z^2 Log[1 - (-1)^(3/8) z^(1/8)] - 63 I z^3 Log[1 - (-1)^(3/8) z^(1/8)] - 153 I Log[1 + (-1)^(3/8) z^(1/8)] - 243 I z Log[1 + (-1)^(3/8) z^(1/8)] - 27 I z^2 Log[1 + (-1)^(3/8) z^(1/8)] + 63 I z^3 Log[1 + (-1)^(3/8) z^(1/8)] + 153 (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] + 243 (-1)^(1/4) z Log[1 - (-1)^(5/8) z^(1/8)] + 27 (-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)] - 153 (-1)^(1/4) Log[1 + (-1)^(5/8) z^(1/8)] - 243 (-1)^(1/4) z Log[1 + (-1)^(5/8) z^(1/8)] - 27 (-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)] + 153 Log[1 - (-1)^(7/8) z^(1/8)] + 243 z Log[1 - (-1)^(7/8) z^(1/8)] + 27 z^2 Log[1 - (-1)^(7/8) z^(1/8)] - 63 z^3 Log[1 - (-1)^(7/8) z^(1/8)] - 153 Log[1 + (-1)^(7/8) z^(1/8)] - 243 z Log[1 + (-1)^(7/8) z^(1/8)] - 27 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 ( 1 8 , 2 ; 33 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["1", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["33", "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 196608 z 25 / 8 ( 425 - 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 + 27 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 2 - 27 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 2 + 27 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 2 - 27 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 2 + 27 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 2 - 27 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 2 + 1808 ( - 1 ) 7 / 8 z 9 / 8 + 243 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z - 243 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z + 243 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z - 243 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z + 243 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z - 243 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z + 1224 ( - 1 ) 7 / 8 z 8 - 9 ( - 1 ) 3 / 4 ( z + 1 ) 2 ( 7 z - 17 ) log ( 1 - - 1 8 z 8 ) + 9 ( - 1 ) 3 / 4 ( z + 1 ) 2 ( 7 z - 17 ) log ( - 1 8 z 8 + 1 ) + 153 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 153 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 153 - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 153 - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 153 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 153 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) HypergeometricPFQ 1 8 2 33 8 -1 z -1 1 196608 z 25 8 -1 425 -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 27 1 -1 -1 3 8 z 1 8 z 2 -1 27 -1 3 8 z 1 8 1 z 2 27 -1 1 4 1 -1 -1 5 8 z 1 8 z 2 -1 27 -1 1 4 -1 5 8 z 1 8 1 z 2 27 1 -1 -1 7 8 z 1 8 z 2 -1 27 -1 7 8 z 1 8 1 z 2 1808 -1 7 8 z 9 8 243 1 -1 -1 3 8 z 1 8 z -1 243 -1 3 8 z 1 8 1 z 243 -1 1 4 1 -1 -1 5 8 z 1 8 z -1 243 -1 1 4 -1 5 8 z 1 8 1 z 243 1 -1 -1 7 8 z 1 8 z -1 243 -1 7 8 z 1 8 1 z 1224 -1 7 8 z 1 8 -1 9 -1 3 4 z 1 2 7 z -17 1 -1 -1 1 8 z 1 8 9 -1 3 4 z 1 2 7 z -17 -1 1 8 z 1 8 1 153 1 -1 -1 3 8 z 1 8 -1 153 -1 3 8 z 1 8 1 153 -1 1 4 1 -1 -1 5 8 z 1 8 -1 153 -1 1 4 -1 5 8 z 1 8 1 153 1 -1 -1 7 8 z 1 8 -1 153 -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