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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(18/5), 3, 22/5, -z] == (1/(48828125 z^(17/5))) (17 (-1)^(1/5) (98280 (-1)^(4/5) z^(2/5) + 86580 (-1)^(4/5) z^(7/5) - 163800 (-1)^(4/5) z^(12/5) - 1839775 (-1)^(4/5) z^(17/5) - 3101175 (-1)^(4/5) z^(22/5) - 2072070 (-1)^(4/5) z^(27/5) - 502320 (-1)^(4/5) z^(32/5) + 6552 (-1)^(4/5) (1 + z)^5 (6 - 23 z + 46 z^2) Log[1 + z^(1/5)] + 6552 (-1)^(2/5) (1 + z)^5 (6 - 23 z + 46 z^2) Log[1 - (-1)^(1/5) z^(1/5)] + 39312 Log[1 + (-1)^(2/5) z^(1/5)] + 45864 z Log[1 + (-1)^(2/5) z^(1/5)] - 58968 z^2 Log[1 + (-1)^(2/5) z^(1/5)] + 393120 z^3 Log[1 + (-1)^(2/5) z^(1/5)] + 1703520 z^4 Log[1 + (-1)^(2/5) z^(1/5)] + 2299752 z^5 Log[1 + (-1)^(2/5) z^(1/5)] + 1356264 z^6 Log[1 + (-1)^(2/5) z^(1/5)] + 301392 z^7 Log[1 + (-1)^(2/5) z^(1/5)] - 39312 (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] - 45864 (-1)^(3/5) z Log[1 - (-1)^(3/5) z^(1/5)] + 58968 (-1)^(3/5) z^2 Log[1 - (-1)^(3/5) z^(1/5)] - 393120 (-1)^(3/5) z^3 Log[1 - (-1)^(3/5) z^(1/5)] - 1703520 (-1)^(3/5) z^4 Log[1 - (-1)^(3/5) z^(1/5)] - 2299752 (-1)^(3/5) z^5 Log[1 - (-1)^(3/5) z^(1/5)] - 1356264 (-1)^(3/5) z^6 Log[1 - (-1)^(3/5) z^(1/5)] - 301392 (-1)^(3/5) z^7 Log[1 - (-1)^(3/5) z^(1/5)] - 39312 (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)] - 45864 (-1)^(1/5) z Log[1 + (-1)^(4/5) z^(1/5)] + 58968 (-1)^(1/5) z^2 Log[1 + (-1)^(4/5) z^(1/5)] - 393120 (-1)^(1/5) z^3 Log[1 + (-1)^(4/5) z^(1/5)] - 1703520 (-1)^(1/5) z^4 Log[1 + (-1)^(4/5) z^(1/5)] - 2299752 (-1)^(1/5) z^5 Log[1 + (-1)^(4/5) z^(1/5)] - 1356264 (-1)^(1/5) z^6 Log[1 + (-1)^(4/5) z^(1/5)] - 301392 (-1)^(1/5) z^7 Log[1 + (-1)^(4/5) z^(1/5)]))

 Standard Form

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 MathML Form

 2 F 1 ( - 18 5 , 3 ; 22 5 ; - 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["18", "5"]]], 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["22", "5"], 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 48828125 z 17 / 5 ( 17 - 1 5 ( 301392 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 7 - 301392 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 7 - 301392 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 7 - 502320 ( - 1 ) 4 / 5 z 32 / 5 + 1356264 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 6 - 1356264 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 6 - 1356264 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 6 - 2072070 ( - 1 ) 4 / 5 z 27 / 5 + 2299752 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 5 - 2299752 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 5 - 2299752 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 5 - 3101175 ( - 1 ) 4 / 5 z 22 / 5 + 1703520 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 4 - 1703520 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 4 - 1703520 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 4 - 1839775 ( - 1 ) 4 / 5 z 17 / 5 + 393120 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 3 - 393120 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 3 - 393120 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 3 - 163800 ( - 1 ) 4 / 5 z 12 / 5 - 58968 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 2 + 58968 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 2 + 58968 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 2 + 86580 ( - 1 ) 4 / 5 z 7 / 5 + 45864 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z - 45864 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z - 45864 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z + 98280 ( - 1 ) 4 / 5 z 2 / 5 + 6552 ( - 1 ) 4 / 5 ( z + 1 ) 5 ( 46 z 2 - 23 z + 6 ) log ( z 5 + 1 ) + 6552 ( - 1 ) 2 / 5 ( z + 1 ) 5 ( 46 z 2 - 23 z + 6 ) log ( 1 - - 1 5 z 5 ) + 39312 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - 39312 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - 39312 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) HypergeometricPFQ -1 18 5 3 22 5 -1 z 1 48828125 z 17 5 -1 17 -1 1 5 301392 -1 2 5 z 1 5 1 z 7 -1 301392 -1 3 5 1 -1 -1 3 5 z 1 5 z 7 -1 301392 -1 1 5 -1 4 5 z 1 5 1 z 7 -1 502320 -1 4 5 z 32 5 1356264 -1 2 5 z 1 5 1 z 6 -1 1356264 -1 3 5 1 -1 -1 3 5 z 1 5 z 6 -1 1356264 -1 1 5 -1 4 5 z 1 5 1 z 6 -1 2072070 -1 4 5 z 27 5 2299752 -1 2 5 z 1 5 1 z 5 -1 2299752 -1 3 5 1 -1 -1 3 5 z 1 5 z 5 -1 2299752 -1 1 5 -1 4 5 z 1 5 1 z 5 -1 3101175 -1 4 5 z 22 5 1703520 -1 2 5 z 1 5 1 z 4 -1 1703520 -1 3 5 1 -1 -1 3 5 z 1 5 z 4 -1 1703520 -1 1 5 -1 4 5 z 1 5 1 z 4 -1 1839775 -1 4 5 z 17 5 393120 -1 2 5 z 1 5 1 z 3 -1 393120 -1 3 5 1 -1 -1 3 5 z 1 5 z 3 -1 393120 -1 1 5 -1 4 5 z 1 5 1 z 3 -1 163800 -1 4 5 z 12 5 -1 58968 -1 2 5 z 1 5 1 z 2 58968 -1 3 5 1 -1 -1 3 5 z 1 5 z 2 58968 -1 1 5 -1 4 5 z 1 5 1 z 2 86580 -1 4 5 z 7 5 45864 -1 2 5 z 1 5 1 z -1 45864 -1 3 5 1 -1 -1 3 5 z 1 5 z -1 45864 -1 1 5 -1 4 5 z 1 5 1 z 98280 -1 4 5 z 2 5 6552 -1 4 5 z 1 5 46 z 2 -1 23 z 6 z 1 5 1 6552 -1 2 5 z 1 5 46 z 2 -1 23 z 6 1 -1 -1 1 5 z 1 5 39312 -1 2 5 z 1 5 1 -1 39312 -1 3 5 1 -1 -1 3 5 z 1 5 -1 39312 -1 1 5 -1 4 5 z 1 5 1 [/itex]

 Rule Form

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

 2007-05-02