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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.as2b.01

 Input Form

 Hypergeometric2F1[-(17/5), 2, 23/5, z] == (1/(68359375 z^(18/5))) (39 (-1)^(1/5) (61880 (-1)^(4/5) z^(3/5) - 243355 (-1)^(4/5) z^(8/5) + 214200 (-1)^(4/5) z^(13/5) - 1358350 (-1)^(4/5) z^(18/5) + 1582700 (-1)^(4/5) z^(23/5) - 804780 (-1)^(4/5) z^(28/5) + 157080 (-1)^(4/5) z^(33/5) + 2856 (-1)^(4/5) (-1 + z)^6 (13 + 22 z) Log[1 - z^(1/5)] - 2856 (-1)^(1/5) (-1 + z)^6 (13 + 22 z) Log[1 + (-1)^(1/5) z^(1/5)] - 37128 (-1)^(3/5) Log[1 - (-1)^(2/5) z^(1/5)] + 159936 (-1)^(3/5) z Log[1 - (-1)^(2/5) z^(1/5)] - 179928 (-1)^(3/5) z^2 Log[1 - (-1)^(2/5) z^(1/5)] - 199920 (-1)^(3/5) z^3 Log[1 - (-1)^(2/5) z^(1/5)] + 699720 (-1)^(3/5) z^4 Log[1 - (-1)^(2/5) z^(1/5)] - 719712 (-1)^(3/5) z^5 Log[1 - (-1)^(2/5) z^(1/5)] + 339864 (-1)^(3/5) z^6 Log[1 - (-1)^(2/5) z^(1/5)] - 62832 (-1)^(3/5) z^7 Log[1 - (-1)^(2/5) z^(1/5)] + 37128 Log[1 + (-1)^(3/5) z^(1/5)] - 159936 z Log[1 + (-1)^(3/5) z^(1/5)] + 179928 z^2 Log[1 + (-1)^(3/5) z^(1/5)] + 199920 z^3 Log[1 + (-1)^(3/5) z^(1/5)] - 699720 z^4 Log[1 + (-1)^(3/5) z^(1/5)] + 719712 z^5 Log[1 + (-1)^(3/5) z^(1/5)] - 339864 z^6 Log[1 + (-1)^(3/5) z^(1/5)] + 62832 z^7 Log[1 + (-1)^(3/5) z^(1/5)] + 37128 (-1)^(2/5) Log[1 - (-1)^(4/5) z^(1/5)] - 159936 (-1)^(2/5) z Log[1 - (-1)^(4/5) z^(1/5)] + 179928 (-1)^(2/5) z^2 Log[1 - (-1)^(4/5) z^(1/5)] + 199920 (-1)^(2/5) z^3 Log[1 - (-1)^(4/5) z^(1/5)] - 699720 (-1)^(2/5) z^4 Log[1 - (-1)^(4/5) z^(1/5)] + 719712 (-1)^(2/5) z^5 Log[1 - (-1)^(4/5) z^(1/5)] - 339864 (-1)^(2/5) z^6 Log[1 - (-1)^(4/5) z^(1/5)] + 62832 (-1)^(2/5) z^7 Log[1 - (-1)^(4/5) z^(1/5)]))

 Standard Form

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 MathML Form

 2 F 1 ( - 17 5 , 2 ; 23 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["17", "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["23", "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 18 / 5 ( 39 - 1 5 ( - 62832 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 7 + 62832 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 7 + 62832 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 7 + 157080 ( - 1 ) 4 / 5 z 33 / 5 + 339864 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 6 - 339864 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 6 - 339864 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 6 - 804780 ( - 1 ) 4 / 5 z 28 / 5 - 719712 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 5 + 719712 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 5 + 719712 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 5 + 1582700 ( - 1 ) 4 / 5 z 23 / 5 + 699720 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 4 - 699720 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 4 - 699720 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 4 - 1358350 ( - 1 ) 4 / 5 z 18 / 5 - 199920 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 3 + 199920 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 3 + 199920 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 3 + 214200 ( - 1 ) 4 / 5 z 13 / 5 - 179928 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z 2 + 179928 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z 2 + 179928 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z 2 - 243355 ( - 1 ) 4 / 5 z 8 / 5 + 159936 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) z - 159936 log ( ( - 1 ) 3 / 5 z 5 + 1 ) z - 159936 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) z + 61880 ( - 1 ) 4 / 5 z 3 / 5 + 2856 ( - 1 ) 4 / 5 ( z - 1 ) 6 ( 22 z + 13 ) log ( 1 - z 5 ) - 2856 - 1 5 ( z - 1 ) 6 ( 22 z + 13 ) log ( - 1 5 z 5 + 1 ) - 37128 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 2 / 5 z 5 ) + 37128 log ( ( - 1 ) 3 / 5 z 5 + 1 ) + 37128 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 4 / 5 z 5 ) ) ) HypergeometricPFQ -1 17 5 2 23 5 z 1 68359375 z 18 5 -1 39 -1 1 5 -62832 -1 3 5 1 -1 -1 2 5 z 1 5 z 7 62832 -1 3 5 z 1 5 1 z 7 62832 -1 2 5 1 -1 -1 4 5 z 1 5 z 7 157080 -1 4 5 z 33 5 339864 -1 3 5 1 -1 -1 2 5 z 1 5 z 6 -1 339864 -1 3 5 z 1 5 1 z 6 -1 339864 -1 2 5 1 -1 -1 4 5 z 1 5 z 6 -1 804780 -1 4 5 z 28 5 -1 719712 -1 3 5 1 -1 -1 2 5 z 1 5 z 5 719712 -1 3 5 z 1 5 1 z 5 719712 -1 2 5 1 -1 -1 4 5 z 1 5 z 5 1582700 -1 4 5 z 23 5 699720 -1 3 5 1 -1 -1 2 5 z 1 5 z 4 -1 699720 -1 3 5 z 1 5 1 z 4 -1 699720 -1 2 5 1 -1 -1 4 5 z 1 5 z 4 -1 1358350 -1 4 5 z 18 5 -1 199920 -1 3 5 1 -1 -1 2 5 z 1 5 z 3 199920 -1 3 5 z 1 5 1 z 3 199920 -1 2 5 1 -1 -1 4 5 z 1 5 z 3 214200 -1 4 5 z 13 5 -1 179928 -1 3 5 1 -1 -1 2 5 z 1 5 z 2 179928 -1 3 5 z 1 5 1 z 2 179928 -1 2 5 1 -1 -1 4 5 z 1 5 z 2 -1 243355 -1 4 5 z 8 5 159936 -1 3 5 1 -1 -1 2 5 z 1 5 z -1 159936 -1 3 5 z 1 5 1 z -1 159936 -1 2 5 1 -1 -1 4 5 z 1 5 z 61880 -1 4 5 z 3 5 2856 -1 4 5 z -1 6 22 z 13 1 -1 z 1 5 -1 2856 -1 1 5 z -1 6 22 z 13 -1 1 5 z 1 5 1 -1 37128 -1 3 5 1 -1 -1 2 5 z 1 5 37128 -1 3 5 z 1 5 1 37128 -1 2 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