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variants of this functions
LaguerreL






Mathematica Notation

Traditional Notation









Polynomials > LaguerreL[n,lambda,z] > Summation > Infinite summation





http://functions.wolfram.com/05.08.23.0012.01









  


  










Input Form





Sum[((t (1 - t)^\[Mu] E^((\[Alpha] z t)/(1 - t)))^k/(1 + \[Alpha] k)) LaguerreL[k, \[Lambda] + \[Mu] k, z (1 + \[Alpha] k)], {k, 0, Infinity}] == (E^((z t)/(t - 1)) Hypergeometric2F1[(1 + \[Mu] - \[Alpha] \[Lambda])/ \[Alpha], 1, (\[Alpha] + 1)/\[Alpha], t])/(1 - t)^\[Lambda]










Standard Form





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MathML Form







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</mo> <mi> &#945; </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mi> k </mi> <mo> &#8290; </mo> <mi> &#945; </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> t </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> &#955; </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mfrac> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mi> t </mi> </mrow> <mrow> <mi> t </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> </msup> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mi> &#945; </mi> </mrow> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mi> &#956; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mi> &#945; </mi> </mfrac> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ; 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</ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> &#945; </ci> <ci> z </ci> <ci> t </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> t </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <ci> k </ci> </apply> <apply> <ci> LaguerreL </ci> <ci> k </ci> <apply> <plus /> <ci> &#955; </ci> <apply> <times /> <ci> k </ci> <ci> &#956; </ci> </apply> </apply> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> k </ci> <ci> &#945; </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> k </ci> <ci> &#945; </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> t </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#955; 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Rule Form





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





2002-12-18





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