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variants of this functions
NorlundB






Mathematica Notation

Traditional Notation









Polynomials > NorlundB[n,α] > Series representations > Generalized power series > Expansions at z==0





http://functions.wolfram.com/05.16.06.0007.01









  


  










Input Form





NorlundB[n, z] \[Proportional] KroneckerDelta[n] + z ((1/2) KroneckerDelta[n - 1] + (n + 1 - 2 Floor[n/2]) n! Sum[(((-1)^j Binomial[n, j])/j) Subscript[p, j, n], {j, 1, n}] - (n - 2 Floor[n/2]) n! Sum[(((-1)^j Binomial[n, j])/j) (1/j - HarmonicNumber[n]) Subscript[p, j, n] z, {j, 1, n}]) (1 + O[z]) /; Subscript[p, j, 0] == 1 && Subscript[p, j, k] == (1/k) Sum[(j m - k + m) Subscript[a, m] Subscript[p, j, k - m], {m, 1, k}] && Subscript[a, k] == 1/(k + 1)! && Element[k, Integers] && k >= 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





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