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HermiteH

  • HermiteH[ n , x ] gives the Hermite polynomial .
  • Mathematical function (see Section A.3.10).
  • Explicit polynomials are given for non-negative integers n.
  • The Hermite polynomials satisfy the differential equation .
  • They are orthogonal polynomials with weight function in the interval .
  • HermiteH[ n , x ] is an entire function of x with no branch cut discontinuities.
  • See the Mathematica book: Section 3.2.9.
  • See also: LaguerreL.

    Further Examples

    This is the derivative.

    In[1]:=

    Out[1]=

    This is the second derivative

    In[2]:=

    Out[2]=

    This verifies the defining differential equation for n = 3.

    In[3]:=

    Out[3]=

    This is a series expansion around .

    In[4]:=

    Out[4]=