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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.br5f.01

 Input Form

 Hypergeometric2F1[-(11/8), 1, 37/8, z] == (1/(10485760 z^(29/8))) (29 (-1)^(1/4) (-24024 (-1)^(3/4) z^(5/8) + 110880 (-1)^(3/4) z^(13/8) - 199760 (-1)^(3/4) z^(21/8) - 189280 (-1)^(3/4) z^(29/8) + 40040 (-1)^(3/4) z^(37/8) + 15015 (-1)^(3/4) (-1 + z)^5 Log[1 - z^(1/8)] + 15015 (-1)^(1/4) (-1 + z)^5 Log[1 - I z^(1/8)] + 15015 (-1)^(1/4) Log[1 + I z^(1/8)] - 75075 (-1)^(1/4) z Log[1 + I z^(1/8)] + 150150 (-1)^(1/4) z^2 Log[1 + I z^(1/8)] - 150150 (-1)^(1/4) z^3 Log[1 + I z^(1/8)] + 75075 (-1)^(1/4) z^4 Log[1 + I z^(1/8)] - 15015 (-1)^(1/4) z^5 Log[1 + I z^(1/8)] + 15015 (-1)^(3/4) Log[1 + z^(1/8)] - 75075 (-1)^(3/4) z Log[1 + z^(1/8)] + 150150 (-1)^(3/4) z^2 Log[1 + z^(1/8)] - 150150 (-1)^(3/4) z^3 Log[1 + z^(1/8)] + 75075 (-1)^(3/4) z^4 Log[1 + z^(1/8)] - 15015 (-1)^(3/4) z^5 Log[1 + z^(1/8)] + 15015 I Log[1 - (-1)^(1/4) z^(1/8)] - 75075 I z Log[1 - (-1)^(1/4) z^(1/8)] + 150150 I z^2 Log[1 - (-1)^(1/4) z^(1/8)] - 150150 I z^3 Log[1 - (-1)^(1/4) z^(1/8)] + 75075 I z^4 Log[1 - (-1)^(1/4) z^(1/8)] - 15015 I z^5 Log[1 - (-1)^(1/4) z^(1/8)] - 15015 I Log[1 + (-1)^(1/4) z^(1/8)] + 75075 I z Log[1 + (-1)^(1/4) z^(1/8)] - 150150 I z^2 Log[1 + (-1)^(1/4) z^(1/8)] + 150150 I z^3 Log[1 + (-1)^(1/4) z^(1/8)] - 75075 I z^4 Log[1 + (-1)^(1/4) z^(1/8)] + 15015 I z^5 Log[1 + (-1)^(1/4) z^(1/8)] + 15015 Log[1 - (-1)^(3/4) z^(1/8)] - 75075 z Log[1 - (-1)^(3/4) z^(1/8)] + 150150 z^2 Log[1 - (-1)^(3/4) z^(1/8)] - 150150 z^3 Log[1 - (-1)^(3/4) z^(1/8)] + 75075 z^4 Log[1 - (-1)^(3/4) z^(1/8)] - 15015 z^5 Log[1 - (-1)^(3/4) z^(1/8)] - 15015 Log[1 + (-1)^(3/4) z^(1/8)] + 75075 z Log[1 + (-1)^(3/4) z^(1/8)] - 150150 z^2 Log[1 + (-1)^(3/4) z^(1/8)] + 150150 z^3 Log[1 + (-1)^(3/4) z^(1/8)] - 75075 z^4 Log[1 + (-1)^(3/4) z^(1/8)] + 15015 z^5 Log[1 + (-1)^(3/4) z^(1/8)]))

 Standard Form

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 MathML Form

 2 F 1 ( - 11 8 , 1 ; 37 8 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["11", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["37", "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 10485760 z 29 / 8 ( 29 - 1 4 ( 15015 ( - 1 ) 3 / 4 log ( 1 - z 8 ) ( z - 1 ) 5 + 15015 - 1 4 log ( 1 - z 8 ) ( z - 1 ) 5 + 40040 ( - 1 ) 3 / 4 z 37 / 8 - 189280 ( - 1 ) 3 / 4 z 29 / 8 - 199760 ( - 1 ) 3 / 4 z 21 / 8 + 110880 ( - 1 ) 3 / 4 z 13 / 8 - 15015 - 1 4 z 5 log ( z 8 + 1 ) + 75075 - 1 4 z 4 log ( z 8 + 1 ) - 150150 - 1 4 z 3 log ( z 8 + 1 ) + 150150 - 1 4 z 2 log ( z 8 + 1 ) - 75075 - 1 4 z log ( z 8 + 1 ) + 15015 - 1 4 log ( z 8 + 1 ) - 15015 ( - 1 ) 3 / 4 z 5 log ( z 8 + 1 ) + 75075 ( - 1 ) 3 / 4 z 4 log ( z 8 + 1 ) - 150150 ( - 1 ) 3 / 4 z 3 log ( z 8 + 1 ) + 150150 ( - 1 ) 3 / 4 z 2 log ( z 8 + 1 ) - 75075 ( - 1 ) 3 / 4 z log ( z 8 + 1 ) + 15015 ( - 1 ) 3 / 4 log ( z 8 + 1 ) - 15015 z 5 log ( 1 - - 1 4 z 8 ) + 75075 z 4 log ( 1 - - 1 4 z 8 ) - 150150 z 3 log ( 1 - - 1 4 z 8 ) + 150150 z 2 log ( 1 - - 1 4 z 8 ) - 75075 z log ( 1 - - 1 4 z 8 ) + 15015 log ( 1 - - 1 4 z 8 ) + 15015 z 5 log ( - 1 4 z 8 + 1 ) - 75075 z 4 log ( - 1 4 z 8 + 1 ) + 150150 z 3 log ( - 1 4 z 8 + 1 ) - 150150 z 2 log ( - 1 4 z 8 + 1 ) + 75075 z log ( - 1 4 z 8 + 1 ) - 15015 log ( - 1 4 z 8 + 1 ) - 15015 z 5 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 75075 z 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 150150 z 3 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 150150 z 2 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 75075 z log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 15015 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 15015 z 5 log ( ( - 1 ) 3 / 4 z 8 + 1 ) - 75075 z 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 150150 z 3 log ( ( - 1 ) 3 / 4 z 8 + 1 ) - 150150 z 2 log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 75075 z log ( ( - 1 ) 3 / 4 z 8 + 1 ) - 15015 log ( ( - 1 ) 3 / 4 z 8 + 1 ) - 24024 ( - 1 ) 3 / 4 z 5 / 8 ) ) HypergeometricPFQ -1 11 8 1 37 8 z 1 10485760 z 29 8 -1 29 -1 1 4 15015 -1 3 4 1 -1 z 1 8 z -1 5 15015 -1 1 4 1 -1 z 1 8 z -1 5 40040 -1 3 4 z 37 8 -1 189280 -1 3 4 z 29 8 -1 199760 -1 3 4 z 21 8 110880 -1 3 4 z 13 8 -1 15015 -1 1 4 z 5 z 1 8 1 75075 -1 1 4 z 4 z 1 8 1 -1 150150 -1 1 4 z 3 z 1 8 1 150150 -1 1 4 z 2 z 1 8 1 -1 75075 -1 1 4 z z 1 8 1 15015 -1 1 4 z 1 8 1 -1 15015 -1 3 4 z 5 z 1 8 1 75075 -1 3 4 z 4 z 1 8 1 -1 150150 -1 3 4 z 3 z 1 8 1 150150 -1 3 4 z 2 z 1 8 1 -1 75075 -1 3 4 z z 1 8 1 15015 -1 3 4 z 1 8 1 -1 15015 z 5 1 -1 -1 1 4 z 1 8 75075 z 4 1 -1 -1 1 4 z 1 8 -1 150150 z 3 1 -1 -1 1 4 z 1 8 150150 z 2 1 -1 -1 1 4 z 1 8 -1 75075 z 1 -1 -1 1 4 z 1 8 15015 1 -1 -1 1 4 z 1 8 15015 z 5 -1 1 4 z 1 8 1 -1 75075 z 4 -1 1 4 z 1 8 1 150150 z 3 -1 1 4 z 1 8 1 -1 150150 z 2 -1 1 4 z 1 8 1 75075 z -1 1 4 z 1 8 1 -1 15015 -1 1 4 z 1 8 1 -1 15015 z 5 1 -1 -1 3 4 z 1 8 75075 z 4 1 -1 -1 3 4 z 1 8 -1 150150 z 3 1 -1 -1 3 4 z 1 8 150150 z 2 1 -1 -1 3 4 z 1 8 -1 75075 z 1 -1 -1 3 4 z 1 8 15015 1 -1 -1 3 4 z 1 8 15015 z 5 -1 3 4 z 1 8 1 -1 75075 z 4 -1 3 4 z 1 8 1 150150 z 3 -1 3 4 z 1 8 1 -1 150150 z 2 -1 3 4 z 1 8 1 75075 z -1 3 4 z 1 8 1 -1 15015 -1 3 4 z 1 8 1 -1 24024 -1 3 4 z 5 8 [/itex]

 Rule Form

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

 2007-05-02