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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(24/5), 6, 16/5, -z] == (1/(30517578125 z^(11/5))) (11 (-861840 z^(1/5) + 19247760 z^(6/5) + 1395566275 z^(11/5) + 8579383200 z^(16/5) + 18923213400 z^(21/5) + 17627569960 z^(26/5) + 5907111210 z^(31/5) + 9576 (1 + z)^2 (18 - 435 z + 29580 z^2 + 288405 z^3 + 704990 z^4 + 493493 z^5) Log[1 + z^(1/5)] + 9576 (-1)^(4/5) (1 + z)^2 (18 - 435 z + 29580 z^2 + 288405 z^3 + 704990 z^4 + 493493 z^5) Log[1 - (-1)^(1/5) z^(1/5)] - 172368 (-1)^(3/5) Log[1 + (-1)^(2/5) z^(1/5)] + 3820824 (-1)^(3/5) z Log[1 + (-1)^(2/5) z^(1/5)] - 275099328 (-1)^(3/5) z^2 Log[1 + (-1)^(2/5) z^(1/5)] - 3324116880 (-1)^(3/5) z^3 Log[1 + (-1)^(2/5) z^(1/5)] - 12557774880 (-1)^(3/5) z^4 Log[1 + (-1)^(2/5) z^(1/5)] - 20989423728 (-1)^(3/5) z^5 Log[1 + (-1)^(2/5) z^(1/5)] - 16202362176 (-1)^(3/5) z^6 Log[1 + (-1)^(2/5) z^(1/5)] - 4725688968 (-1)^(3/5) z^7 Log[1 + (-1)^(2/5) z^(1/5)] + 172368 (-1)^(2/5) Log[1 - (-1)^(3/5) z^(1/5)] - 3820824 (-1)^(2/5) z Log[1 - (-1)^(3/5) z^(1/5)] + 275099328 (-1)^(2/5) z^2 Log[1 - (-1)^(3/5) z^(1/5)] + 3324116880 (-1)^(2/5) z^3 Log[1 - (-1)^(3/5) z^(1/5)] + 12557774880 (-1)^(2/5) z^4 Log[1 - (-1)^(3/5) z^(1/5)] + 20989423728 (-1)^(2/5) z^5 Log[1 - (-1)^(3/5) z^(1/5)] + 16202362176 (-1)^(2/5) z^6 Log[1 - (-1)^(3/5) z^(1/5)] + 4725688968 (-1)^(2/5) z^7 Log[1 - (-1)^(3/5) z^(1/5)] - 172368 (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)] + 3820824 (-1)^(1/5) z Log[1 + (-1)^(4/5) z^(1/5)] - 275099328 (-1)^(1/5) z^2 Log[1 + (-1)^(4/5) z^(1/5)] - 3324116880 (-1)^(1/5) z^3 Log[1 + (-1)^(4/5) z^(1/5)] - 12557774880 (-1)^(1/5) z^4 Log[1 + (-1)^(4/5) z^(1/5)] - 20989423728 (-1)^(1/5) z^5 Log[1 + (-1)^(4/5) z^(1/5)] - 16202362176 (-1)^(1/5) z^6 Log[1 + (-1)^(4/5) z^(1/5)] - 4725688968 (-1)^(1/5) z^7 Log[1 + (-1)^(4/5) z^(1/5)]))

 Standard Form

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 MathML Form

 2 F 1 ( - 24 5 , 6 ; 16 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["24", "5"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["16", "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 30517578125 z 11 / 5 ( 11 ( - 4725688968 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 7 + 4725688968 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 7 - 4725688968 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 7 + 5907111210 z 31 / 5 - 16202362176 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 6 + 16202362176 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 6 - 16202362176 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 6 + 17627569960 z 26 / 5 - 20989423728 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 5 + 20989423728 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 5 - 20989423728 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 5 + 18923213400 z 21 / 5 - 12557774880 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 4 + 12557774880 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 4 - 12557774880 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 4 + 8579383200 z 16 / 5 - 3324116880 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 3 + 3324116880 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 3 - 3324116880 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 3 + 1395566275 z 11 / 5 - 275099328 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 2 + 275099328 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 2 - 275099328 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 2 + 19247760 z 6 / 5 + 3820824 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z - 3820824 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z + 3820824 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z - 861840 z 5 + 9576 ( z + 1 ) 2 ( 493493 z 5 + 704990 z 4 + 288405 z 3 + 29580 z 2 - 435 z + 18 ) log ( z 5 + 1 ) + 9576 ( - 1 ) 4 / 5 ( z + 1 ) 2 ( 493493 z 5 + 704990 z 4 + 288405 z 3 + 29580 z 2 - 435 z + 18 ) log ( 1 - - 1 5 z 5 ) - 172368 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + 172368 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - 172368 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) HypergeometricPFQ -1 24 5 6 16 5 -1 z 1 30517578125 z 11 5 -1 11 -4725688968 -1 3 5 -1 2 5 z 1 5 1 z 7 4725688968 -1 2 5 1 -1 -1 3 5 z 1 5 z 7 -1 4725688968 -1 1 5 -1 4 5 z 1 5 1 z 7 5907111210 z 31 5 -1 16202362176 -1 3 5 -1 2 5 z 1 5 1 z 6 16202362176 -1 2 5 1 -1 -1 3 5 z 1 5 z 6 -1 16202362176 -1 1 5 -1 4 5 z 1 5 1 z 6 17627569960 z 26 5 -1 20989423728 -1 3 5 -1 2 5 z 1 5 1 z 5 20989423728 -1 2 5 1 -1 -1 3 5 z 1 5 z 5 -1 20989423728 -1 1 5 -1 4 5 z 1 5 1 z 5 18923213400 z 21 5 -1 12557774880 -1 3 5 -1 2 5 z 1 5 1 z 4 12557774880 -1 2 5 1 -1 -1 3 5 z 1 5 z 4 -1 12557774880 -1 1 5 -1 4 5 z 1 5 1 z 4 8579383200 z 16 5 -1 3324116880 -1 3 5 -1 2 5 z 1 5 1 z 3 3324116880 -1 2 5 1 -1 -1 3 5 z 1 5 z 3 -1 3324116880 -1 1 5 -1 4 5 z 1 5 1 z 3 1395566275 z 11 5 -1 275099328 -1 3 5 -1 2 5 z 1 5 1 z 2 275099328 -1 2 5 1 -1 -1 3 5 z 1 5 z 2 -1 275099328 -1 1 5 -1 4 5 z 1 5 1 z 2 19247760 z 6 5 3820824 -1 3 5 -1 2 5 z 1 5 1 z -1 3820824 -1 2 5 1 -1 -1 3 5 z 1 5 z 3820824 -1 1 5 -1 4 5 z 1 5 1 z -1 861840 z 1 5 9576 z 1 2 493493 z 5 704990 z 4 288405 z 3 29580 z 2 -1 435 z 18 z 1 5 1 9576 -1 4 5 z 1 2 493493 z 5 704990 z 4 288405 z 3 29580 z 2 -1 435 z 18 1 -1 -1 1 5 z 1 5 -1 172368 -1 3 5 -1 2 5 z 1 5 1 172368 -1 2 5 1 -1 -1 3 5 z 1 5 -1 172368 -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