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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(18/5), 2, 22/5, z] == (1/(68359375 z^(17/5))) (17 (-1)^(1/5) (196560 (-1)^(4/5) z^(2/5) - 746460 (-1)^(4/5) z^(7/5) + 491400 (-1)^(4/5) z^(12/5) - 2215325 (-1)^(4/5) z^(17/5) + 2523150 (-1)^(4/5) z^(22/5) - 1281735 (-1)^(4/5) z^(27/5) + 251160 (-1)^(4/5) z^(32/5) + 6552 (-1)^(4/5) (-1 + z)^6 (12 + 23 z) Log[1 - z^(1/5)] + 6552 (-1)^(2/5) (-1 + z)^6 (12 + 23 z) Log[1 + (-1)^(1/5) z^(1/5)] + 78624 Log[1 - (-1)^(2/5) z^(1/5)] - 321048 z Log[1 - (-1)^(2/5) z^(1/5)] + 275184 z^2 Log[1 - (-1)^(2/5) z^(1/5)] + 687960 z^3 Log[1 - (-1)^(2/5) z^(1/5)] - 1834560 z^4 Log[1 - (-1)^(2/5) z^(1/5)] + 1788696 z^5 Log[1 - (-1)^(2/5) z^(1/5)] - 825552 z^6 Log[1 - (-1)^(2/5) z^(1/5)] + 150696 z^7 Log[1 - (-1)^(2/5) z^(1/5)] - 78624 (-1)^(3/5) Log[1 + (-1)^(3/5) z^(1/5)] + 321048 (-1)^(3/5) z Log[1 + (-1)^(3/5) z^(1/5)] - 275184 (-1)^(3/5) z^2 Log[1 + (-1)^(3/5) z^(1/5)] - 687960 (-1)^(3/5) z^3 Log[1 + (-1)^(3/5) z^(1/5)] + 1834560 (-1)^(3/5) z^4 Log[1 + (-1)^(3/5) z^(1/5)] - 1788696 (-1)^(3/5) z^5 Log[1 + (-1)^(3/5) z^(1/5)] + 825552 (-1)^(3/5) z^6 Log[1 + (-1)^(3/5) z^(1/5)] - 150696 (-1)^(3/5) z^7 Log[1 + (-1)^(3/5) z^(1/5)] - 78624 (-1)^(1/5) Log[1 - (-1)^(4/5) z^(1/5)] + 321048 (-1)^(1/5) z Log[1 - (-1)^(4/5) z^(1/5)] - 275184 (-1)^(1/5) z^2 Log[1 - (-1)^(4/5) z^(1/5)] - 687960 (-1)^(1/5) z^3 Log[1 - (-1)^(4/5) z^(1/5)] + 1834560 (-1)^(1/5) z^4 Log[1 - (-1)^(4/5) z^(1/5)] - 1788696 (-1)^(1/5) z^5 Log[1 - (-1)^(4/5) z^(1/5)] + 825552 (-1)^(1/5) z^6 Log[1 - (-1)^(4/5) z^(1/5)] - 150696 (-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 , 2 ; 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["2", 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["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 68359375 z 17 / 5 ( 17 - 1 5 ( 150696 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 7 - 150696 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 7 - 150696 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 7 + 251160 ( - 1 ) 4 / 5 z 32 / 5 - 825552 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 6 + 825552 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 6 + 825552 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 6 - 1281735 ( - 1 ) 4 / 5 z 27 / 5 + 1788696 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 5 - 1788696 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 5 - 1788696 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 5 + 2523150 ( - 1 ) 4 / 5 z 22 / 5 - 1834560 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 4 + 1834560 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 4 + 1834560 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 4 - 2215325 ( - 1 ) 4 / 5 z 17 / 5 + 687960 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 3 - 687960 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 3 - 687960 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 3 + 491400 ( - 1 ) 4 / 5 z 12 / 5 + 275184 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 2 - 275184 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 2 - 275184 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 2 - 746460 ( - 1 ) 4 / 5 z 7 / 5 - 321048 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z + 321048 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z + 321048 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z + 196560 ( - 1 ) 4 / 5 z 2 / 5 + 6552 ( - 1 ) 4 / 5 ( z - 1 ) 6 ( 23 z + 12 ) log ( 1 - z 5 ) + 6552 ( - 1 ) 2 / 5 ( z - 1 ) 6 ( 23 z + 12 ) log ( - 1 5 z 5 + 1 ) + 78624 log ( 1 - ( - 1 ) 2 / 5 z 5 ) - 78624 ( - 1 ) 3 / 5 log ( ( - 1 ) 3 / 5 z 5 + 1 ) - 78624 - 1 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) HypergeometricPFQ -1 18 5 2 22 5 z 1 68359375 z 17 5 -1 17 -1 1 5 150696 1 -1 -1 2 5 z 1 5 z 7 -1 150696 -1 3 5 -1 3 5 z 1 5 1 z 7 -1 150696 -1 1 5 1 -1 -1 4 5 z 1 5 z 7 251160 -1 4 5 z 32 5 -1 825552 1 -1 -1 2 5 z 1 5 z 6 825552 -1 3 5 -1 3 5 z 1 5 1 z 6 825552 -1 1 5 1 -1 -1 4 5 z 1 5 z 6 -1 1281735 -1 4 5 z 27 5 1788696 1 -1 -1 2 5 z 1 5 z 5 -1 1788696 -1 3 5 -1 3 5 z 1 5 1 z 5 -1 1788696 -1 1 5 1 -1 -1 4 5 z 1 5 z 5 2523150 -1 4 5 z 22 5 -1 1834560 1 -1 -1 2 5 z 1 5 z 4 1834560 -1 3 5 -1 3 5 z 1 5 1 z 4 1834560 -1 1 5 1 -1 -1 4 5 z 1 5 z 4 -1 2215325 -1 4 5 z 17 5 687960 1 -1 -1 2 5 z 1 5 z 3 -1 687960 -1 3 5 -1 3 5 z 1 5 1 z 3 -1 687960 -1 1 5 1 -1 -1 4 5 z 1 5 z 3 491400 -1 4 5 z 12 5 275184 1 -1 -1 2 5 z 1 5 z 2 -1 275184 -1 3 5 -1 3 5 z 1 5 1 z 2 -1 275184 -1 1 5 1 -1 -1 4 5 z 1 5 z 2 -1 746460 -1 4 5 z 7 5 -1 321048 1 -1 -1 2 5 z 1 5 z 321048 -1 3 5 -1 3 5 z 1 5 1 z 321048 -1 1 5 1 -1 -1 4 5 z 1 5 z 196560 -1 4 5 z 2 5 6552 -1 4 5 z -1 6 23 z 12 1 -1 z 1 5 6552 -1 2 5 z -1 6 23 z 12 -1 1 5 z 1 5 1 78624 1 -1 -1 2 5 z 1 5 -1 78624 -1 3 5 -1 3 5 z 1 5 1 -1 78624 -1 1 5 1 -1 -1 4 5 z 1 5 [/itex]

 Rule Form

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

 2007-05-02