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variants of this functions
JacobiP




Mathematica Notation

Traditional Notation









Polynomials > JacobiP[n,a,b,z] > Summation > Infinite summation





http://functions.wolfram.com/05.06.23.0003.01









  


  








Input Form





Sum[((Pochhammer[a, k] Pochhammer[1 + \[Alpha] + \[Beta] - a, k])/ (Pochhammer[1 + \[Alpha], k] Pochhammer[1 + \[Beta], k])) JacobiP[k, \[Alpha], \[Beta], z] t^k, {k, 0, Infinity}] == Hypergeometric2F1[a, 1 + \[Alpha] + \[Beta] - a, 1 + \[Alpha], (1/2) (1 - t - Sqrt[1 - 2 z t + t^2])] Hypergeometric2F1[a, 1 + \[Alpha] + \[Beta] - a, 1 + \[Beta], (1/2) (1 + t - Sqrt[1 - 2 z t + t^2])]








Standard Form





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MathML Form







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</ci> <ci> &#946; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> &#946; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> t </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> t </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <ci> t </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </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