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variants of this functions
GegenbauerC






Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,lambda,z] > Series representations > Generalized power series > Expansions at z==-1 > For the function itself > General case





http://functions.wolfram.com/07.14.06.0013.02









  


  










Input Form





GegenbauerC[\[Nu], \[Lambda], z] \[Proportional] ((Cos[Pi (\[Nu] + \[Lambda])] Sec[Pi \[Lambda]] Gamma[\[Nu] + 2 \[Lambda]])/ (Gamma[\[Nu] + 1] Gamma[2 \[Lambda]])) (1 - ((\[Nu] (2 \[Lambda] + \[Nu]))/(2 \[Lambda] + 1)) (z + 1) - ((\[Nu] (1 - \[Nu]) (2 \[Lambda] + \[Nu]) (1 + 2 \[Lambda] + \[Nu]))/ (2 (2 \[Lambda] + 1) (2 \[Lambda] + 3))) (z + 1)^2 - \[Ellipsis]) - ((2^(1/2 - \[Lambda]) Sin[\[Nu] Pi] Gamma[\[Lambda] - 1/2])/ (Sqrt[Pi] Gamma[\[Lambda]])) (z + 1)^(1/2 - \[Lambda]) (1 + (((1 - 2 \[Lambda] - 2 \[Nu]) (1 + 2 \[Lambda] + 2 \[Nu]))/ (4 (3 - 2 \[Lambda]))) (z + 1) + (((1 - 2 \[Lambda] - 2 \[Nu]) (3 - 2 \[Lambda] - 2 \[Nu]) (1 + 2 \[Lambda] + 2 \[Nu]) (3 + 2 \[Lambda] + 2 \[Nu]))/ (32 (3 - 2 \[Lambda]) (5 - 2 \[Lambda]))) (z + 1)^2 + \[Ellipsis]) /; (z -> -1) && !Element[\[Lambda] + 1/2, Integers]










Standard Form





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MathML Form







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</ci> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <ci> Rule </ci> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <notin /> <apply> <plus /> <ci> &#955; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





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