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1
Formal definition
2
Recursion relations
3
Usage
4
Notes
Hermite number
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From Wikipedia, the free encyclopedia
Formal definition[edit]
The numbers Hn = Hn(0), where Hn(x) is a Hermite polynomial of order n, may be called Hermite numbers.[1]
The first Hermite numbers are:
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Recursion relations[edit]
Are obtained from recursion relations of Hermitian polynomials for x = 0:
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Since H0 = 1 and H1 = 0 one can construct a closed formula for Hn:
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where (n - 1)!! = 1 × 3 × ... × (n - 1).
From the generating function of Hermitian polynomials it follows that
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Reference [1] gives a formal power series:
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where formally the n-th power of H, Hn, is the n-th Hermite number, Hn. (See Umbral calculus.)
Retrieved from "https://en.wikipedia.org/w/index.php?title=Hermite_number&oldid=1047823488"
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