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variants of this functions
JacobiP






Mathematica Notation

Traditional Notation









Polynomials > JacobiP[n,a,b,z] > Series representations > Generalized power series > Expansions at a==0





http://functions.wolfram.com/05.06.06.0039.01









  


  










Input Form





JacobiP[n, a, b, z] \[Proportional] JacobiP[n, 0, b, z] + Sum[(1/(b + k + n + 1)) (JacobiP[n, 0, b, z] + (((b + 1 + 2 k) Pochhammer[b + k + 1, n - k])/ ((n - k) Pochhammer[b + k + 1, n - k])) JacobiP[k, 0, b, z]) a, {k, 0, n - 1}] + ((1/(2 n!)) Sum[(Pochhammer[-n, k + 2]/(k + 2)!) Sum[(-1)^(j + k + n) (j + 1) (j + 2) (1 + b + n)^j Pochhammer[3 + b + k, -k + n - 2] StirlingS1[k + 2, j + 2] ((1 + z)/2)^(k + 2), {j, 0, k}], {k, 0, n - 2}]) a^2 + \[Ellipsis] /; (a -> 0)










Standard Form





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MathML Form







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</ci> </apply> </apply> <apply> <ci> Rule </ci> <ci> a </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02