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variants of this functions
NorlundB






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/05.17.06.0020.01









  


  










Input Form





NorlundB[n, \[Alpha], z] \[Proportional] z^n UnitStep[n] + \[Alpha] ((n/2) z^(n - 1) UnitStep[n - 1] + Sum[Binomial[n, k] z^k (n - k + 1 - 2 Floor[(n - k)/2]) (n - k)! Sum[(((-1)^j Binomial[n - k, j])/j) Subscript[p, j, n - k], {j, 1, n - k}], {k, 0, n}] - Sum[Binomial[n, k] z^k (n - k - 2 Floor[(n - k)/2]) (n - k)! Sum[(((-1)^j Binomial[n - k, j])/j) (1/j - HarmonicNumber[n - k]) Subscript[p, j, n - k] \[Alpha], {j, 1, n - k}], {k, 0, n}]) (1 + O[\[Alpha]]) /; 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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</ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> O </ci> <ci> &#945; </ci> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> j </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> j </ci> <ci> k </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> k </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> m </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> k </ci> </uplimit> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> j </ci> <ci> m </ci> </apply> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> m </ci> </apply> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> j </ci> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <factorial /> <apply> <plus /> <ci> k </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <in /> <ci> k </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





© 1998- Wolfram Research, Inc.