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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ce2w.01

 Input Form

 Hypergeometric2F1[6, 6, -(39/8), z] == (1/50956866389278720) (-((1/(-1 + z)^16) (16 (-3184804149329920 + 74475420107407360 z - 907171309950074880 z^2 + 8088265919152783360 z^3 - 66381123092098318336 z^4 + 735433774046323408896 z^5 + 9460859037930817256425 z^6 + 17433776510320286561600 z^7 + 9320064447067224321600 z^8 + 1449683714228519045120 z^9 + 44405301669122744320 z^10))) - (1/(1 - z)^(135/8)) (491074533339390 (-1)^(3/8) (-1 + (-1)^(1/4)) z^(47/8) (112724073 + 409905720 z + 416412160 z^2 + 140759040 z^3 + 14254080 z^4 + 262144 z^5) ArcTan[1 - (z^(1/8) Cos[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Sin[Pi/8])/(1 - z)^(1/8))]) - (1/(1 - z)^(135/8)) (491074533339390 (-1)^(3/8) (-1 + (-1)^(1/4)) z^(47/8) (112724073 + 409905720 z + 416412160 z^2 + 140759040 z^3 + 14254080 z^4 + 262144 z^5) ArcTan[1 + (z^(1/8) Cos[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Sin[Pi/8])/(1 - z)^(1/8))]) - (1/(1 - z)^(135/8)) (491074533339390 (-1)^(1/8) (-1 + (-1)^(3/4)) z^(47/8) (112724073 + 409905720 z + 416412160 z^2 + 140759040 z^3 + 14254080 z^4 + 262144 z^5) ArcTan[1 - (z^(1/8) Sin[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Cos[Pi/8])/(1 - z)^(1/8))]) - (1/(1 - z)^(135/8)) (491074533339390 (-1)^(1/8) (-1 + (-1)^(3/4)) z^(47/8) (112724073 + 409905720 z + 416412160 z^2 + 140759040 z^3 + 14254080 z^4 + 262144 z^5) ArcTan[1 + (z^(1/8) Sin[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Cos[Pi/8])/(1 - z)^(1/8))]) - (1/(1 - z)^(135/8)) (245537266669695 (-1)^(1/8) (-1 + (-1)^(3/4)) z^(47/8) (112724073 + 409905720 z + 416412160 z^2 + 140759040 z^3 + 14254080 z^4 + 262144 z^5) Log[1 + z^(1/4)/(1 - z)^(1/4) - (2 z^(1/8) Cos[Pi/8])/(1 - z)^(1/8)]) + (1/(1 - z)^(135/8)) (245537266669695 (-1)^(1/8) (-1 + (-1)^(3/4)) z^(47/8) (112724073 + 409905720 z + 416412160 z^2 + 140759040 z^3 + 14254080 z^4 + 262144 z^5) Log[1 + z^(1/4)/(1 - z)^(1/4) + (2 z^(1/8) Cos[Pi/8])/(1 - z)^(1/8)]) - (1/(1 - z)^(135/8)) (245537266669695 (-1)^(3/8) (-1 + (-1)^(1/4)) z^(47/8) (112724073 + 409905720 z + 416412160 z^2 + 140759040 z^3 + 14254080 z^4 + 262144 z^5) Log[1 + z^(1/4)/(1 - z)^(1/4) - (2 z^(1/8) Sin[Pi/8])/(1 - z)^(1/8)]) + (1/(1 - z)^(135/8)) (245537266669695 (-1)^(3/8) (-1 + (-1)^(1/4)) z^(47/8) (112724073 + 409905720 z + 416412160 z^2 + 140759040 z^3 + 14254080 z^4 + 262144 z^5) Log[1 + z^(1/4)/(1 - z)^(1/4) + (2 z^(1/8) Sin[Pi/8])/(1 - z)^(1/8)]))

 Standard Form

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 MathML Form

 2 F 1 ( 6 , 6 ; - 39 8 ; 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["39", "8"]]], 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 50956866389278720 ( - 1 ( 1 - z ) 135 / 8 ( 491074533339390 ( - 1 ) 3 / 8 ( - 1 + - 1 4 ) ( 262144 z 5 + 14254080 z 4 + 140759040 z 3 + 416412160 z 2 + 409905720 z + 112724073 ) tan - 1 ( 1 - z 8 cos ( π 8 ) 1 - z 8 , - z 8 sin ( π 8 ) 1 - z 8 ) z 47 / 8 ) - 1 ( 1 - z ) 135 / 8 ( 491074533339390 ( - 1 ) 3 / 8 ( - 1 + - 1 4 ) ( 262144 z 5 + 14254080 z 4 + 140759040 z 3 + 416412160 z 2 + 409905720 z + 112724073 ) tan - 1 ( cos ( π 8 ) z 8 1 - z 8 + 1 , - z 8 sin ( π 8 ) 1 - z 8 ) z 47 / 8 ) - 1 ( 1 - z ) 135 / 8 ( 491074533339390 - 1 8 ( - 1 + ( - 1 ) 3 / 4 ) ( 262144 z 5 + 14254080 z 4 + 140759040 z 3 + 416412160 z 2 + 409905720 z + 112724073 ) tan - 1 ( 1 - z 8 sin ( π 8 ) 1 - z 8 , - z 8 cos ( π 8 ) 1 - z 8 ) z 47 / 8 ) - 1 ( 1 - z ) 135 / 8 ( 491074533339390 - 1 8 ( - 1 + ( - 1 ) 3 / 4 ) ( 262144 z 5 + 14254080 z 4 + 140759040 z 3 + 416412160 z 2 + 409905720 z + 112724073 ) tan - 1 ( sin ( π 8 ) z 8 1 - z 8 + 1 , - z 8 cos ( π 8 ) 1 - z 8 ) z 47 / 8 ) - 1 ( 1 - z ) 135 / 8 ( 245537266669695 - 1 8 ( - 1 + ( - 1 ) 3 / 4 ) ( 262144 z 5 + 14254080 z 4 + 140759040 z 3 + 416412160 z 2 + 409905720 z + 112724073 ) log ( z 4 1 - z 4 - 2 cos ( π 8 ) z 8 1 - z 8 + 1 ) z 47 / 8 ) + 1 ( 1 - z ) 135 / 8 ( 245537266669695 - 1 8 ( - 1 + ( - 1 ) 3 / 4 ) ( 262144 z 5 + 14254080 z 4 + 140759040 z 3 + 416412160 z 2 + 409905720 z + 112724073 ) log ( z 4 1 - z 4 + 2 cos ( π 8 ) z 8 1 - z 8 + 1 ) z 47 / 8 ) - 1 ( 1 - z ) 135 / 8 ( 245537266669695 ( - 1 ) 3 / 8 ( - 1 + - 1 4 ) ( 262144 z 5 + 14254080 z 4 + 140759040 z 3 + 416412160 z 2 + 409905720 z + 112724073 ) log ( z 4 1 - z 4 - 2 sin ( π 8 ) z 8 1 - z 8 + 1 ) z 47 / 8 ) + 1 ( 1 - z ) 135 / 8 ( 245537266669695 ( - 1 ) 3 / 8 ( - 1 + - 1 4 ) ( 262144 z 5 + 14254080 z 4 + 140759040 z 3 + 416412160 z 2 + 409905720 z + 112724073 ) log ( z 4 1 - z 4 + 2 sin ( π 8 ) z 8 1 - z 8 + 1 ) z 47 / 8 ) - 1 ( z - 1 ) 16 ( 16 ( 44405301669122744320 z 10 + 1449683714228519045120 z 9 + 9320064447067224321600 z 8 + 17433776510320286561600 z 7 + 9460859037930817256425 z 6 + 735433774046323408896 z 5 - 66381123092098318336 z 4 + 8088265919152783360 z 3 - 907171309950074880 z 2 + 74475420107407360 z - 3184804149329920 ) ) ) HypergeometricPFQ 6 6 -1 39 8 z 1 50956866389278720 -1 1 1 -1 z 135 8 -1 491074533339390 -1 3 8 -1 -1 1 4 262144 z 5 14254080 z 4 140759040 z 3 416412160 z 2 409905720 z 112724073 1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 z 47 8 -1 1 1 -1 z 135 8 -1 491074533339390 -1 3 8 -1 -1 1 4 262144 z 5 14254080 z 4 140759040 z 3 416412160 z 2 409905720 z 112724073 8 -1 z 1 8 1 -1 z 1 8 -1 1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 z 47 8 -1 1 1 -1 z 135 8 -1 491074533339390 -1 1 8 -1 -1 3 4 262144 z 5 14254080 z 4 140759040 z 3 416412160 z 2 409905720 z 112724073 1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 z 47 8 -1 1 1 -1 z 135 8 -1 491074533339390 -1 1 8 -1 -1 3 4 262144 z 5 14254080 z 4 140759040 z 3 416412160 z 2 409905720 z 112724073 8 -1 z 1 8 1 -1 z 1 8 -1 1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 z 47 8 -1 1 1 -1 z 135 8 -1 245537266669695 -1 1 8 -1 -1 3 4 262144 z 5 14254080 z 4 140759040 z 3 416412160 z 2 409905720 z 112724073 z 1 4 1 -1 z 1 4 -1 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 z 47 8 1 1 -1 z 135 8 -1 245537266669695 -1 1 8 -1 -1 3 4 262144 z 5 14254080 z 4 140759040 z 3 416412160 z 2 409905720 z 112724073 z 1 4 1 -1 z 1 4 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 z 47 8 -1 1 1 -1 z 135 8 -1 245537266669695 -1 3 8 -1 -1 1 4 262144 z 5 14254080 z 4 140759040 z 3 416412160 z 2 409905720 z 112724073 z 1 4 1 -1 z 1 4 -1 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 z 47 8 1 1 -1 z 135 8 -1 245537266669695 -1 3 8 -1 -1 1 4 262144 z 5 14254080 z 4 140759040 z 3 416412160 z 2 409905720 z 112724073 z 1 4 1 -1 z 1 4 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 z 47 8 -1 1 z -1 16 -1 16 44405301669122744320 z 10 1449683714228519045120 z 9 9320064447067224321600 z 8 17433776510320286561600 z 7 9460859037930817256425 z 6 735433774046323408896 z 5 -1 66381123092098318336 z 4 8088265919152783360 z 3 -1 907171309950074880 z 2 74475420107407360 z -3184804149329920 [/itex]

 Rule Form

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

 2007-05-02