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variants of this functions
GegenbauerC






Mathematica Notation

Traditional Notation









Polynomials > GegenbauerC[n,lambda,z] > Transformations > Addition formulas





http://functions.wolfram.com/05.09.16.0004.01









  


  










Input Form





GegenbauerC[n, \[Alpha], Cos[Subscript[\[Theta], 0]]] == Sum[(((Pochhammer[\[Alpha], k] (n - k)!) Sin[\[Theta]]^k Sin[\[CurlyTheta]]^k)/(Pochhammer[\[Alpha] - 1/2, k] Pochhammer[2 \[Alpha] + 2 k, n - k])) GegenbauerC[n - k, \[Alpha] + k, Cos[\[Theta]]] GegenbauerC[n - k, \[Alpha] + k, Cos[\[CurlyTheta]]] GegenbauerC[k, \[Alpha] - 1/2, Cos[\[Phi]]], {k, 0, n}] /; Element[n, Integers] && n >= 0 && Cos[Subscript[\[Theta], 0]] == Cos[\[Theta]] Cos[\[CurlyTheta]] + Sin[\[Theta]] Sin[\[CurlyTheta]] Cos[\[Phi]]










Standard Form





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MathML Form







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</ci> </apply> <apply> <cos /> <apply> <ci> Subscript </ci> <ci> &#952; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <times /> <apply> <ci> Pochhammer </ci> <ci> &#945; </ci> <ci> k </ci> </apply> <apply> <factorial /> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Pochhammer </ci> <apply> <plus /> <ci> &#945; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#945; </ci> </apply> </apply> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <sin /> <ci> &#952; 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</ci> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <ci> &#8469; </ci> </apply> <apply> <eq /> <apply> <cos /> <apply> <ci> Subscript </ci> <ci> &#952; </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <cos /> <ci> &#952; </ci> </apply> <apply> <cos /> <ci> &#977; </ci> </apply> </apply> <apply> <times /> <apply> <cos /> <ci> &#981; </ci> </apply> <apply> <sin /> <ci> &#952; </ci> </apply> <apply> <sin /> <ci> &#977; </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18





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