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variants of this functions
HermiteH




Mathematica Notation

Traditional Notation









Polynomials > HermiteH[n,z] > Series representations > Generalized power series > Expansions at n==infinity





http://functions.wolfram.com/05.01.06.0021.01









  


  








Input Form





HermiteH[n, z] \[Proportional] (-1)^Floor[n/2] (Floor[n/2] + (-1)^(n - 1)/2)! E^(z^2/2) 2^n z^(n - 2 Floor[n/2]) Sum[(Subscript[A, k] z^(2 k) Hypergeometric0F1Regularized[ (-1)^(n - 1)/2 + k + 1, (-z^2) (Floor[n/2] + ((-1)^(n - 1) + 2)/4)])/ 2^k, {k, 0, Infinity}] /; (n -> Infinity) && Subscript[A, 0] == 1 && Subscript[A, 1] == 0 && Subscript[A, 2] == ((-1)^(n - 1) + 2)/4 && Subscript[A, m] == ((2 m + (-1)^(n - 1) - 2)/(2 m)) Subscript[A, m - 2] - (2 Floor[n/2] + (-1)^(n - 1)/2 + 1) Subscript[A, m - 3] && Element[m, Integers] && m > 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