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http://functions.wolfram.com/07.14.06.0043.01
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GegenbauerC[\[Nu], \[Lambda], z] \[Proportional]
((2^(1 - 2 \[Lambda]) Cos[Pi (\[Lambda] + \[Nu])] Sin[Pi \[Nu]])/
(Pi^(3/2) Gamma[\[Lambda]])) ((-I) Pi^(3/2) 4^\[Lambda]
E^(I Pi (1/2 - \[Lambda]) Floor[Arg[z - x]/(2 Pi)]) Csc[Pi \[Nu]]
Floor[Arg[z - x]/(2 Pi)] Gamma[\[Lambda]] GegenbauerC[\[Nu], \[Lambda],
-x] - Exp[Pi I (1 - 2 \[Lambda]) Floor[Arg[z - x]/(2 Pi)]]
MeijerG[{{1 + \[Nu], 1 - 2 \[Lambda] - \[Nu]}, {}},
{{0, 1/2 - \[Lambda]}, {}}, (1/2) (1 + x)] +
(1/2) (2 Pi I E^(I Pi (1/2 - \[Lambda]) Floor[Arg[z - x]/(2 Pi)])
Floor[Arg[z - x]/(2 Pi)] Gamma[1 - \[Nu]]
Gamma[1 + 2 \[Lambda] + \[Nu]] Hypergeometric2F1Regularized[1 - \[Nu],
1 + 2 \[Lambda] + \[Nu], 3/2 + \[Lambda], (1/2) (1 + x)] +
Exp[Pi I (1 - 2 \[Lambda]) Floor[Arg[z - x]/(2 Pi)]]
MeijerG[{{\[Nu], -2 \[Lambda] - \[Nu]}, {}}, {{0, -(1/2) - \[Lambda]},
{}}, (1/2) (1 + x)]) (z - x) +
(1/8) (2 Pi I E^(I Pi (1/2 - \[Lambda]) Floor[Arg[z - x]/(2 Pi)])
Floor[Arg[z - x]/(2 Pi)] Gamma[2 - \[Nu]]
Gamma[2 + 2 \[Lambda] + \[Nu]] Hypergeometric2F1Regularized[2 - \[Nu],
2 + 2 \[Lambda] + \[Nu], 5/2 + \[Lambda], (1/2) (1 + x)] -
Exp[Pi I (1 - 2 \[Lambda]) Floor[Arg[z - x]/(2 Pi)]]
MeijerG[{{-1 + \[Nu], -1 - 2 \[Lambda] - \[Nu]}, {}},
{{0, -(3/2) - \[Lambda]}, {}}, (1/2) (1 + x)]) (z - x)^2 +
O[(z - x)^3]) /; Element[x, Reals] && x < -1
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msubsup> <mi> C </mi> <mi> ν </mi> <mi> λ </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mfrac> <mrow> <msup> <mn> 2 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> λ </mi> </mrow> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> λ </mi> <mo> + </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <msup> <mi> π </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> λ </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <msup> <mi> π </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mn> 4 </mn> <mi> λ </mi> </msup> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> - </mo> <mi> λ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mi> x </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> csc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> λ </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> arg 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Date Added to functions.wolfram.com (modification date)
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