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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.as8i.01

 Input Form

 Hypergeometric2F1[-(17/5), 5, 13/5, -z] == -((1/(48828125 z^(8/5))) (24 (-1)^(1/5) (4165 (-1)^(4/5) z^(3/5) + 1914935 (-1)^(4/5) z^(8/5) + 10751565 (-1)^(4/5) z^(13/5) + 17536860 (-1)^(4/5) z^(18/5) + 8717940 (-1)^(4/5) z^(23/5) + 119 (-1)^(4/5) (-21 + 595 z + 13090 z^2 + 50490 z^3 + 67320 z^4 + 29304 z^5) Log[1 + z^(1/5)] - 119 (-1)^(1/5) (-21 + 595 z + 13090 z^2 + 50490 z^3 + 67320 z^4 + 29304 z^5) Log[1 - (-1)^(1/5) z^(1/5)] + 2499 (-1)^(3/5) Log[1 + (-1)^(2/5) z^(1/5)] - 70805 (-1)^(3/5) z Log[1 + (-1)^(2/5) z^(1/5)] - 1557710 (-1)^(3/5) z^2 Log[1 + (-1)^(2/5) z^(1/5)] - 6008310 (-1)^(3/5) z^3 Log[1 + (-1)^(2/5) z^(1/5)] - 8011080 (-1)^(3/5) z^4 Log[1 + (-1)^(2/5) z^(1/5)] - 3487176 (-1)^(3/5) z^5 Log[1 + (-1)^(2/5) z^(1/5)] - 2499 Log[1 - (-1)^(3/5) z^(1/5)] + 70805 z Log[1 - (-1)^(3/5) z^(1/5)] + 1557710 z^2 Log[1 - (-1)^(3/5) z^(1/5)] + 6008310 z^3 Log[1 - (-1)^(3/5) z^(1/5)] + 8011080 z^4 Log[1 - (-1)^(3/5) z^(1/5)] + 3487176 z^5 Log[1 - (-1)^(3/5) z^(1/5)] - 2499 (-1)^(2/5) Log[1 + (-1)^(4/5) z^(1/5)] + 70805 (-1)^(2/5) z Log[1 + (-1)^(4/5) z^(1/5)] + 1557710 (-1)^(2/5) z^2 Log[1 + (-1)^(4/5) z^(1/5)] + 6008310 (-1)^(2/5) z^3 Log[1 + (-1)^(4/5) z^(1/5)] + 8011080 (-1)^(2/5) z^4 Log[1 + (-1)^(4/5) z^(1/5)] + 3487176 (-1)^(2/5) z^5 Log[1 + (-1)^(4/5) z^(1/5)])))

 Standard Form

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 MathML Form

 2 F 1 ( - 17 5 , 5 ; 13 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["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["13", "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 8 / 5 ( 24 - 1 5 ( - 3487176 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 5 + 3487176 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 5 + 3487176 ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 5 + 8717940 ( - 1 ) 4 / 5 z 23 / 5 - 8011080 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 4 + 8011080 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 4 + 8011080 ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 4 + 17536860 ( - 1 ) 4 / 5 z 18 / 5 - 6008310 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 3 + 6008310 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 3 + 6008310 ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 3 + 10751565 ( - 1 ) 4 / 5 z 13 / 5 - 1557710 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 2 + 1557710 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 2 + 1557710 ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 2 + 1914935 ( - 1 ) 4 / 5 z 8 / 5 - 70805 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z + 70805 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z + 70805 ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z + 4165 ( - 1 ) 4 / 5 z 3 / 5 + 119 ( - 1 ) 4 / 5 ( 29304 z 5 + 67320 z 4 + 50490 z 3 + 13090 z 2 + 595 z - 21 ) log ( z 5 + 1 ) - 119 - 1 5 ( 29304 z 5 + 67320 z 4 + 50490 z 3 + 13090 z 2 + 595 z - 21 ) log ( 1 - - 1 5 z 5 ) + 2499 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - 2499 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - 2499 ( - 1 ) 2 / 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) HypergeometricPFQ -1 17 5 5 13 5 -1 z -1 1 48828125 z 8 5 -1 24 -1 1 5 -3487176 -1 3 5 -1 2 5 z 1 5 1 z 5 3487176 1 -1 -1 3 5 z 1 5 z 5 3487176 -1 2 5 -1 4 5 z 1 5 1 z 5 8717940 -1 4 5 z 23 5 -1 8011080 -1 3 5 -1 2 5 z 1 5 1 z 4 8011080 1 -1 -1 3 5 z 1 5 z 4 8011080 -1 2 5 -1 4 5 z 1 5 1 z 4 17536860 -1 4 5 z 18 5 -1 6008310 -1 3 5 -1 2 5 z 1 5 1 z 3 6008310 1 -1 -1 3 5 z 1 5 z 3 6008310 -1 2 5 -1 4 5 z 1 5 1 z 3 10751565 -1 4 5 z 13 5 -1 1557710 -1 3 5 -1 2 5 z 1 5 1 z 2 1557710 1 -1 -1 3 5 z 1 5 z 2 1557710 -1 2 5 -1 4 5 z 1 5 1 z 2 1914935 -1 4 5 z 8 5 -1 70805 -1 3 5 -1 2 5 z 1 5 1 z 70805 1 -1 -1 3 5 z 1 5 z 70805 -1 2 5 -1 4 5 z 1 5 1 z 4165 -1 4 5 z 3 5 119 -1 4 5 29304 z 5 67320 z 4 50490 z 3 13090 z 2 595 z -21 z 1 5 1 -1 119 -1 1 5 29304 z 5 67320 z 4 50490 z 3 13090 z 2 595 z -21 1 -1 -1 1 5 z 1 5 2499 -1 3 5 -1 2 5 z 1 5 1 -1 2499 1 -1 -1 3 5 z 1 5 -1 2499 -1 2 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