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 GegenbauerC

 http://functions.wolfram.com/05.09.06.0054.01

 Input Form

 GegenbauerC[n, \[Lambda], z] \[Proportional] ((2^(1 - \[Lambda]) n^(\[Lambda] - 1))/(Gamma[\[Lambda]] (1 - z^2)^(\[Lambda]/2))) (Cos[(Pi \[Lambda])/2 - (n + \[Lambda]) ArcCos[z]] + (((-1 + \[Lambda]) \[Lambda])/(2 n)) (Cos[(Pi \[Lambda])/2 - (n + \[Lambda]) ArcCos[z]] + Sin[(Pi \[Lambda])/2 - (-1 + n + \[Lambda]) ArcCos[z]]/Sqrt[1 - z^2]) + (((1 - \[Lambda]) (2 - \[Lambda]) \[Lambda])/(24 n^2)) (-((3 (1 + \[Lambda]) Cos[(1/2) Pi (2 + \[Lambda]) - (-2 + n + \[Lambda]) ArcCos[z]])/(-1 + z^2)) - (6 (-1 + \[Lambda]) Cos[(1/2) Pi (1 + \[Lambda]) - (-1 + n + \[Lambda]) ArcCos[z]])/Sqrt[1 - z^2] + (-1 + 3 \[Lambda]) Cos[(Pi \[Lambda])/2 - (n + \[Lambda]) ArcCos[z]]) + \[Ellipsis]) /; (n -> Infinity)

 Standard Form

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 MathML Form

 C n λ ( z ) 2 1 - λ n λ - 1 Γ ( λ ) ( 1 - z 2 ) λ / 2 ( cos ( π λ 2 - ( n + λ ) cos - 1 ( z ) ) + ( λ - 1 ) λ 2 n ( cos ( π λ 2 - ( n + λ ) cos - 1 ( z ) ) + 1 1 - z 2 sin ( π λ 2 - ( n + λ - 1 ) cos - 1 ( z ) ) ) + ( 1 - λ ) ( 2 - λ ) λ 24 n 2 ( ( 3 λ - 1 ) cos ( π λ 2 - ( n + λ ) cos - 1 ( z ) ) - 6 ( λ - 1 ) 1 - z 2 cos ( 1 2 π ( λ + 1 ) - ( n + λ - 1 ) cos - 1 ( z ) ) - 3 ( λ + 1 ) z 2 - 1 cos ( 1 2 π ( λ + 2 ) - ( n + λ - 2 ) cos - 1 ( z ) ) ) + ) /; ( n "\[Rule]" ) Condition Proportional Subscript C n λ z 2 1 -1 λ n λ -1 Gamma λ 1 -1 z 2 λ 2 -1 -1 λ 2 -1 -1 n λ z λ -1 λ 2 n -1 λ 2 -1 -1 n λ z 1 1 -1 z 2 1 2 -1 λ 2 -1 -1 n λ -1 z 1 -1 λ 2 -1 λ λ 24 n 2 -1 3 λ -1 λ 2 -1 -1 n λ z -1 6 λ -1 1 -1 z 2 1 2 -1 1 2 λ 1 -1 n λ -1 z -1 3 λ 1 z 2 -1 -1 1 2 λ 2 -1 n λ -2 cos -1 z Rule n [/itex]

 Rule Form

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

 2007-05-02