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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.br9z.01

 Input Form

 Hypergeometric2F1[-(11/8), 2, 45/8, z] == (1/(4026531840 z^(37/8))) (1073 (-1)^(1/4) (-696696 (-1)^(3/4) z^(5/8) + 2759064 (-1)^(3/4) z^(13/8) - 3686320 (-1)^(3/4) z^(21/8) + 1201200 (-1)^(3/4) z^(29/8) - 2435160 (-1)^(3/4) z^(37/8) + 760760 (-1)^(3/4) z^(45/8) + 15015 (-1)^(3/4) (-1 + z)^5 (29 + 19 z) Log[1 - z^(1/8)] + 15015 (-1)^(1/4) (-1 + z)^5 (29 + 19 z) Log[1 - I z^(1/8)] + 435435 (-1)^(1/4) Log[1 + I z^(1/8)] - 1891890 (-1)^(1/4) z Log[1 + I z^(1/8)] + 2927925 (-1)^(1/4) z^2 Log[1 + I z^(1/8)] - 1501500 (-1)^(1/4) z^3 Log[1 + I z^(1/8)] - 675675 (-1)^(1/4) z^4 Log[1 + I z^(1/8)] + 990990 (-1)^(1/4) z^5 Log[1 + I z^(1/8)] - 285285 (-1)^(1/4) z^6 Log[1 + I z^(1/8)] + 435435 (-1)^(3/4) Log[1 + z^(1/8)] - 1891890 (-1)^(3/4) z Log[1 + z^(1/8)] + 2927925 (-1)^(3/4) z^2 Log[1 + z^(1/8)] - 1501500 (-1)^(3/4) z^3 Log[1 + z^(1/8)] - 675675 (-1)^(3/4) z^4 Log[1 + z^(1/8)] + 990990 (-1)^(3/4) z^5 Log[1 + z^(1/8)] - 285285 (-1)^(3/4) z^6 Log[1 + z^(1/8)] + 435435 I Log[1 - (-1)^(1/4) z^(1/8)] - 1891890 I z Log[1 - (-1)^(1/4) z^(1/8)] + 2927925 I z^2 Log[1 - (-1)^(1/4) z^(1/8)] - 1501500 I z^3 Log[1 - (-1)^(1/4) z^(1/8)] - 675675 I z^4 Log[1 - (-1)^(1/4) z^(1/8)] + 990990 I z^5 Log[1 - (-1)^(1/4) z^(1/8)] - 285285 I z^6 Log[1 - (-1)^(1/4) z^(1/8)] - 435435 I Log[1 + (-1)^(1/4) z^(1/8)] + 1891890 I z Log[1 + (-1)^(1/4) z^(1/8)] - 2927925 I z^2 Log[1 + (-1)^(1/4) z^(1/8)] + 1501500 I z^3 Log[1 + (-1)^(1/4) z^(1/8)] + 675675 I z^4 Log[1 + (-1)^(1/4) z^(1/8)] - 990990 I z^5 Log[1 + (-1)^(1/4) z^(1/8)] + 285285 I z^6 Log[1 + (-1)^(1/4) z^(1/8)] + 435435 Log[1 - (-1)^(3/4) z^(1/8)] - 1891890 z Log[1 - (-1)^(3/4) z^(1/8)] + 2927925 z^2 Log[1 - (-1)^(3/4) z^(1/8)] - 1501500 z^3 Log[1 - (-1)^(3/4) z^(1/8)] - 675675 z^4 Log[1 - (-1)^(3/4) z^(1/8)] + 990990 z^5 Log[1 - (-1)^(3/4) z^(1/8)] - 285285 z^6 Log[1 - (-1)^(3/4) z^(1/8)] - 435435 Log[1 + (-1)^(3/4) z^(1/8)] + 1891890 z Log[1 + (-1)^(3/4) z^(1/8)] - 2927925 z^2 Log[1 + (-1)^(3/4) z^(1/8)] + 1501500 z^3 Log[1 + (-1)^(3/4) z^(1/8)] + 675675 z^4 Log[1 + (-1)^(3/4) z^(1/8)] - 990990 z^5 Log[1 + (-1)^(3/4) z^(1/8)] + 285285 z^6 Log[1 + (-1)^(3/4) z^(1/8)]))

 Standard Form

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 MathML Form

 2 F 1 ( - 11 8 , 2 ; 45 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["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["45", "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 4026531840 z 37 / 8 ( 1073 - 1 4 ( - 285285 - 1 4 log ( z 8 + 1 ) z 6 - 285285 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 6 - 285285 log ( 1 - - 1 4 z 8 ) z 6 + 285285 log ( - 1 4 z 8 + 1 ) z 6 - 285285 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 6 + 285285 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 6 + 760760 ( - 1 ) 3 / 4 z 45 / 8 + 990990 - 1 4 log ( z 8 + 1 ) z 5 + 990990 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 5 + 990990 log ( 1 - - 1 4 z 8 ) z 5 - 990990 log ( - 1 4 z 8 + 1 ) z 5 + 990990 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 5 - 990990 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 5 - 2435160 ( - 1 ) 3 / 4 z 37 / 8 - 675675 - 1 4 log ( z 8 + 1 ) z 4 - 675675 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 4 - 675675 log ( 1 - - 1 4 z 8 ) z 4 + 675675 log ( - 1 4 z 8 + 1 ) z 4 - 675675 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 4 + 675675 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 4 + 1201200 ( - 1 ) 3 / 4 z 29 / 8 - 1501500 - 1 4 log ( z 8 + 1 ) z 3 - 1501500 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 3 - 1501500 log ( 1 - - 1 4 z 8 ) z 3 + 1501500 log ( - 1 4 z 8 + 1 ) z 3 - 1501500 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 3 + 1501500 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 3 - 3686320 ( - 1 ) 3 / 4 z 21 / 8 + 2927925 - 1 4 log ( z 8 + 1 ) z 2 + 2927925 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 2 + 2927925 log ( 1 - - 1 4 z 8 ) z 2 - 2927925 log ( - 1 4 z 8 + 1 ) z 2 + 2927925 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 2 - 2927925 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 2 + 2759064 ( - 1 ) 3 / 4 z 13 / 8 - 1891890 - 1 4 log ( z 8 + 1 ) z - 1891890 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z - 1891890 log ( 1 - - 1 4 z 8 ) z + 1891890 log ( - 1 4 z 8 + 1 ) z - 1891890 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z + 1891890 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z - 696696 ( - 1 ) 3 / 4 z 5 / 8 + 15015 ( - 1 ) 3 / 4 ( z - 1 ) 5 ( 19 z + 29 ) log ( 1 - z 8 ) + 15015 - 1 4 ( z - 1 ) 5 ( 19 z + 29 ) log ( 1 - z 8 ) + 435435 - 1 4 log ( z 8 + 1 ) + 435435 ( - 1 ) 3 / 4 log ( z 8 + 1 ) + 435435 log ( 1 - - 1 4 z 8 ) - 435435 log ( - 1 4 z 8 + 1 ) + 435435 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 435435 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) HypergeometricPFQ -1 11 8 2 45 8 z 1 4026531840 z 37 8 -1 1073 -1 1 4 -285285 -1 1 4 z 1 8 1 z 6 -1 285285 -1 3 4 z 1 8 1 z 6 -1 285285 1 -1 -1 1 4 z 1 8 z 6 285285 -1 1 4 z 1 8 1 z 6 -1 285285 1 -1 -1 3 4 z 1 8 z 6 285285 -1 3 4 z 1 8 1 z 6 760760 -1 3 4 z 45 8 990990 -1 1 4 z 1 8 1 z 5 990990 -1 3 4 z 1 8 1 z 5 990990 1 -1 -1 1 4 z 1 8 z 5 -1 990990 -1 1 4 z 1 8 1 z 5 990990 1 -1 -1 3 4 z 1 8 z 5 -1 990990 -1 3 4 z 1 8 1 z 5 -1 2435160 -1 3 4 z 37 8 -1 675675 -1 1 4 z 1 8 1 z 4 -1 675675 -1 3 4 z 1 8 1 z 4 -1 675675 1 -1 -1 1 4 z 1 8 z 4 675675 -1 1 4 z 1 8 1 z 4 -1 675675 1 -1 -1 3 4 z 1 8 z 4 675675 -1 3 4 z 1 8 1 z 4 1201200 -1 3 4 z 29 8 -1 1501500 -1 1 4 z 1 8 1 z 3 -1 1501500 -1 3 4 z 1 8 1 z 3 -1 1501500 1 -1 -1 1 4 z 1 8 z 3 1501500 -1 1 4 z 1 8 1 z 3 -1 1501500 1 -1 -1 3 4 z 1 8 z 3 1501500 -1 3 4 z 1 8 1 z 3 -1 3686320 -1 3 4 z 21 8 2927925 -1 1 4 z 1 8 1 z 2 2927925 -1 3 4 z 1 8 1 z 2 2927925 1 -1 -1 1 4 z 1 8 z 2 -1 2927925 -1 1 4 z 1 8 1 z 2 2927925 1 -1 -1 3 4 z 1 8 z 2 -1 2927925 -1 3 4 z 1 8 1 z 2 2759064 -1 3 4 z 13 8 -1 1891890 -1 1 4 z 1 8 1 z -1 1891890 -1 3 4 z 1 8 1 z -1 1891890 1 -1 -1 1 4 z 1 8 z 1891890 -1 1 4 z 1 8 1 z -1 1891890 1 -1 -1 3 4 z 1 8 z 1891890 -1 3 4 z 1 8 1 z -1 696696 -1 3 4 z 5 8 15015 -1 3 4 z -1 5 19 z 29 1 -1 z 1 8 15015 -1 1 4 z -1 5 19 z 29 1 -1 z 1 8 435435 -1 1 4 z 1 8 1 435435 -1 3 4 z 1 8 1 435435 1 -1 -1 1 4 z 1 8 -1 435435 -1 1 4 z 1 8 1 435435 1 -1 -1 3 4 z 1 8 -1 435435 -1 3 4 z 1 8 1 [/itex]

 Rule Form

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

 2007-05-02