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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b4js.01

 Input Form

 Hypergeometric2F1[6, 6, -(28/5), z] == -((8589934592 ((1 - z)^(4/5) - (1 - z)^(3/5) z^(1/5) + (1 - z)^(2/5) z^(2/5) - (1 - z)^(1/5) z^(3/5) + z^(4/5))^16 (3065917968750 - 71830078125000 z + 857000244140625 z^2 - 7171947021484375 z^3 + 50396005859375000 z^4 - 364791211914062500 z^5 + 4556785717285156250 z^6 + 35205684913364462882 z^7 + 51408022832476388630 z^8 + 23048704980635594900 z^9 + 3085950176023179875 z^10 + 82188609295701875 z^11))/ (1532958984375 ((1 - z)^(1/5) + z^(1/5)) (2 (1 - z)^(2/5) + (-1 + Sqrt[5]) (1 - z)^(1/5) z^(1/5) + 2 z^(2/5))^17 (2 (1 - z)^(2/5) - (1 + Sqrt[5]) (1 - z)^(1/5) z^(1/5) + 2 z^(2/5))^17 (-1 + z)^17)) + (1/(1220703125 (1 - z)^(88/5))) (165756228 Sqrt[10 - 2 Sqrt[5]] z^(33/5) (10045832 + 33045500 z + 30740000 z^2 + 9606250 z^3 + 906250 z^4 + 15625 z^5) ArcTan[1 - ((1 - Sqrt[5]) z^(1/5))/(4 (1 - z)^(1/5)), -((Sqrt[5/8 + Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))]) - (1/(1220703125 (1 - z)^(88/5))) (165756228 Sqrt[2 (5 + Sqrt[5])] z^(33/5) (10045832 + 33045500 z + 30740000 z^2 + 9606250 z^3 + 906250 z^4 + 15625 z^5) ArcTan[1 - ((1 + Sqrt[5]) z^(1/5))/(4 (1 - z)^(1/5)), -((Sqrt[5/8 - Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))]) - (1/(1220703125 (1 - z)^(88/5))) (331512456 z^(33/5) (10045832 + 33045500 z + 30740000 z^2 + 9606250 z^3 + 906250 z^4 + 15625 z^5) Log[1 + z^(1/5)/(1 - z)^(1/5)]) + (1/(1220703125 (1 - z)^(88/5))) (82878114 (1 + Sqrt[5]) z^(33/5) (10045832 + 33045500 z + 30740000 z^2 + 9606250 z^3 + 906250 z^4 + 15625 z^5) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)]) - (1/(1220703125 (1 - z)^(88/5))) (82878114 (-1 + Sqrt[5]) z^(33/5) (10045832 + 33045500 z + 30740000 z^2 + 9606250 z^3 + 906250 z^4 + 15625 z^5) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])

 Standard Form

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 MathML Form

 2 F 1 ( 6 , 6 ; - 28 5 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["6", 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[RowBox[List["-", FractionBox["28", "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] - ( 8589934592 ( 82188609295701875 z 11 + 3085950176023179875 z 10 + 23048704980635594900 z 9 + 51408022832476388630 z 8 + 35205684913364462882 z 7 + 4556785717285156250 z 6 - 364791211914062500 z 5 + 50396005859375000 z 4 - 7171947021484375 z 3 + 857000244140625 z 2 - 71830078125000 z + 3065917968750 ) ( ( 1 - z ) 4 / 5 - z 5 ( 1 - z ) 3 / 5 + z 2 / 5 ( 1 - z ) 2 / 5 - z 3 / 5 1 - z 5 + z 4 / 5 ) 16 ) / ( 1532958984375 ( 1 - z 5 + z 5 ) ( 2 ( 1 - z ) 2 / 5 + ( - 1 + 5 ) z 5 1 - z 5 + 2 z 2 / 5 ) 17 ( 2 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 1 - z 5 + 2 z 2 / 5 ) 17 ( z - 1 ) 17 ) + 1 1220703125 ( 1 - z ) 88 / 5 ( 165756228 10 - 2 5 z 33 / 5 ( 15625 z 5 + 906250 z 4 + 9606250 z 3 + 30740000 z 2 + 33045500 z + 10045832 ) tan - 1 ( 1 - ( 1 - 5 ) z 5 4 1 - z 5 , - 5 8 + 5 8 z 5 1 - z 5 ) ) - 1 1220703125 ( 1 - z ) 88 / 5 ( 165756228 2 ( 5 + 5 ) z 33 / 5 ( 15625 z 5 + 906250 z 4 + 9606250 z 3 + 30740000 z 2 + 33045500 z + 10045832 ) tan - 1 ( 1 - ( 1 + 5 ) z 5 4 1 - z 5 , - 5 8 - 5 8 z 5 1 - z 5 ) ) - 1 1220703125 ( 1 - z ) 88 / 5 ( 331512456 z 33 / 5 ( 15625 z 5 + 906250 z 4 + 9606250 z 3 + 30740000 z 2 + 33045500 z + 10045832 ) log ( z 5 1 - z 5 + 1 ) ) + 1 1220703125 ( 1 - z ) 88 / 5 ( 82878114 ( 1 + 5 ) z 33 / 5 ( 15625 z 5 + 906250 z 4 + 9606250 z 3 + 30740000 z 2 + 33045500 z + 10045832 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 - 5 ) z 5 2 1 - z 5 + 1 ) ) - 1 1220703125 ( 1 - z ) 88 / 5 ( 82878114 ( - 1 + 5 ) z 33 / 5 ( 15625 z 5 + 906250 z 4 + 9606250 z 3 + 30740000 z 2 + 33045500 z + 10045832 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 2 1 - z 5 + 1 ) ) HypergeometricPFQ 6 6 -1 28 5 z -1 8589934592 82188609295701875 z 11 3085950176023179875 z 10 23048704980635594900 z 9 51408022832476388630 z 8 35205684913364462882 z 7 4556785717285156250 z 6 -1 364791211914062500 z 5 50396005859375000 z 4 -1 7171947021484375 z 3 857000244140625 z 2 -1 71830078125000 z 3065917968750 1 -1 z 4 5 -1 z 1 5 1 -1 z 3 5 z 2 5 1 -1 z 2 5 -1 z 3 5 1 -1 z 1 5 z 4 5 16 1532958984375 1 -1 z 1 5 z 1 5 2 1 -1 z 2 5 -1 5 1 2 z 1 5 1 -1 z 1 5 2 z 2 5 17 2 1 -1 z 2 5 -1 1 5 1 2 z 1 5 1 -1 z 1 5 2 z 2 5 17 z -1 17 -1 1 1220703125 1 -1 z 88 5 -1 165756228 10 -1 2 5 1 2 1 2 z 33 5 15625 z 5 906250 z 4 9606250 z 3 30740000 z 2 33045500 z 10045832 1 -1 1 -1 5 1 2 z 1 5 4 1 -1 z 1 5 -1 -1 5 8 5 1 2 8 -1 1 2 z 1 5 1 -1 z 1 5 -1 -1 1 1220703125 1 -1 z 88 5 -1 165756228 2 5 5 1 2 1 2 z 33 5 15625 z 5 906250 z 4 9606250 z 3 30740000 z 2 33045500 z 10045832 1 -1 1 5 1 2 z 1 5 4 1 -1 z 1 5 -1 -1 5 8 -1 5 1 2 8 -1 1 2 z 1 5 1 -1 z 1 5 -1 -1 1 1220703125 1 -1 z 88 5 -1 331512456 z 33 5 15625 z 5 906250 z 4 9606250 z 3 30740000 z 2 33045500 z 10045832 z 1 5 1 -1 z 1 5 -1 1 1 1220703125 1 -1 z 88 5 -1 82878114 1 5 1 2 z 33 5 15625 z 5 906250 z 4 9606250 z 3 30740000 z 2 33045500 z 10045832 z 2 5 1 -1 z 2 5 -1 -1 1 -1 5 1 2 z 1 5 2 1 -1 z 1 5 -1 1 -1 1 1220703125 1 -1 z 88 5 -1 82878114 -1 5 1 2 z 33 5 15625 z 5 906250 z 4 9606250 z 3 30740000 z 2 33045500 z 10045832 z 2 5 1 -1 z 2 5 -1 -1 1 5 1 2 z 1 5 2 1 -1 z 1 5 -1 1 [/itex]

 Rule Form

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

 2007-05-02