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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(13/5), 3, 22/5, -z] == (1/(19531250 z^(17/5))) (119 (-1)^(1/5) (10920 (-1)^(4/5) z^(2/5) + 7800 (-1)^(4/5) z^(7/5) - 13000 (-1)^(4/5) z^(12/5) - 97850 (-1)^(4/5) z^(17/5) - 108225 (-1)^(4/5) z^(22/5) - 35880 (-1)^(4/5) z^(27/5) + 312 (-1)^(4/5) (1 + z)^4 (14 - 42 z + 69 z^2) Log[1 + z^(1/5)] + 312 (-1)^(2/5) (1 + z)^4 (14 - 42 z + 69 z^2) Log[1 - (-1)^(1/5) z^(1/5)] + 4368 Log[1 + (-1)^(2/5) z^(1/5)] + 4368 z Log[1 + (-1)^(2/5) z^(1/5)] - 4680 z^2 Log[1 + (-1)^(2/5) z^(1/5)] + 24960 z^3 Log[1 + (-1)^(2/5) z^(1/5)] + 81120 z^4 Log[1 + (-1)^(2/5) z^(1/5)] + 73008 z^5 Log[1 + (-1)^(2/5) z^(1/5)] + 21528 z^6 Log[1 + (-1)^(2/5) z^(1/5)] - 4368 (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] - 4368 (-1)^(3/5) z Log[1 - (-1)^(3/5) z^(1/5)] + 4680 (-1)^(3/5) z^2 Log[1 - (-1)^(3/5) z^(1/5)] - 24960 (-1)^(3/5) z^3 Log[1 - (-1)^(3/5) z^(1/5)] - 81120 (-1)^(3/5) z^4 Log[1 - (-1)^(3/5) z^(1/5)] - 73008 (-1)^(3/5) z^5 Log[1 - (-1)^(3/5) z^(1/5)] - 21528 (-1)^(3/5) z^6 Log[1 - (-1)^(3/5) z^(1/5)] - 4368 (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)] - 4368 (-1)^(1/5) z Log[1 + (-1)^(4/5) z^(1/5)] + 4680 (-1)^(1/5) z^2 Log[1 + (-1)^(4/5) z^(1/5)] - 24960 (-1)^(1/5) z^3 Log[1 + (-1)^(4/5) z^(1/5)] - 81120 (-1)^(1/5) z^4 Log[1 + (-1)^(4/5) z^(1/5)] - 73008 (-1)^(1/5) z^5 Log[1 + (-1)^(4/5) z^(1/5)] - 21528 (-1)^(1/5) z^6 Log[1 + (-1)^(4/5) z^(1/5)]))

 Standard Form

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 MathML Form

 2 F 1 ( - 13 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["13", "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 19531250 z 17 / 5 ( 119 - 1 5 ( 21528 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 6 - 21528 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 6 - 21528 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 6 - 35880 ( - 1 ) 4 / 5 z 27 / 5 + 73008 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 5 - 73008 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 5 - 73008 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 5 - 108225 ( - 1 ) 4 / 5 z 22 / 5 + 81120 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 4 - 81120 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 4 - 81120 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 4 - 97850 ( - 1 ) 4 / 5 z 17 / 5 + 24960 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 3 - 24960 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 3 - 24960 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 3 - 13000 ( - 1 ) 4 / 5 z 12 / 5 - 4680 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 2 + 4680 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 2 + 4680 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 2 + 7800 ( - 1 ) 4 / 5 z 7 / 5 + 4368 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z - 4368 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z - 4368 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z + 10920 ( - 1 ) 4 / 5 z 2 / 5 + 312 ( - 1 ) 4 / 5 ( z + 1 ) 4 ( 69 z 2 - 42 z + 14 ) log ( z 5 + 1 ) + 312 ( - 1 ) 2 / 5 ( z + 1 ) 4 ( 69 z 2 - 42 z + 14 ) log ( 1 - - 1 5 z 5 ) + 4368 log ( ( - 1 ) 2 / 5 z 5 + 1 ) - 4368 ( - 1 ) 3 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - 4368 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) HypergeometricPFQ -1 13 5 3 22 5 -1 z 1 19531250 z 17 5 -1 119 -1 1 5 21528 -1 2 5 z 1 5 1 z 6 -1 21528 -1 3 5 1 -1 -1 3 5 z 1 5 z 6 -1 21528 -1 1 5 -1 4 5 z 1 5 1 z 6 -1 35880 -1 4 5 z 27 5 73008 -1 2 5 z 1 5 1 z 5 -1 73008 -1 3 5 1 -1 -1 3 5 z 1 5 z 5 -1 73008 -1 1 5 -1 4 5 z 1 5 1 z 5 -1 108225 -1 4 5 z 22 5 81120 -1 2 5 z 1 5 1 z 4 -1 81120 -1 3 5 1 -1 -1 3 5 z 1 5 z 4 -1 81120 -1 1 5 -1 4 5 z 1 5 1 z 4 -1 97850 -1 4 5 z 17 5 24960 -1 2 5 z 1 5 1 z 3 -1 24960 -1 3 5 1 -1 -1 3 5 z 1 5 z 3 -1 24960 -1 1 5 -1 4 5 z 1 5 1 z 3 -1 13000 -1 4 5 z 12 5 -1 4680 -1 2 5 z 1 5 1 z 2 4680 -1 3 5 1 -1 -1 3 5 z 1 5 z 2 4680 -1 1 5 -1 4 5 z 1 5 1 z 2 7800 -1 4 5 z 7 5 4368 -1 2 5 z 1 5 1 z -1 4368 -1 3 5 1 -1 -1 3 5 z 1 5 z -1 4368 -1 1 5 -1 4 5 z 1 5 1 z 10920 -1 4 5 z 2 5 312 -1 4 5 z 1 4 69 z 2 -1 42 z 14 z 1 5 1 312 -1 2 5 z 1 4 69 z 2 -1 42 z 14 1 -1 -1 1 5 z 1 5 4368 -1 2 5 z 1 5 1 -1 4368 -1 3 5 1 -1 -1 3 5 z 1 5 -1 4368 -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