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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 b==0





http://functions.wolfram.com/05.06.06.0044.01









  


  








Input Form





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








Standard Form





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MathML Form







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Rule Form





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





2007-05-02