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 Documentation / Mathematica / Built-in Functions / Mathematical Functions / Orthogonal Polynomials  /
LaguerreL

  • LaguerreL[ n , x ] gives the Laguerre polynomial .
  • LaguerreL[ n , a , x ] gives the generalized Laguerre polynomial .
  • Mathematical function (see Section A.3.10).
  • Explicit polynomials are given when possible.
  • .
  • The Laguerre polynomials are orthogonal with weight function .
  • They satisfy the differential equation .
  • LaguerreL[ n , x ] is an entire function of x with no branch cut discontinuities.
  • See the Mathematica book: Section 3.2.9.
  • See also: HermiteH.

    Further Examples

    Here are the first 5 Laguerre polynomials.

    In[1]:=

    Out[1]//TableForm=

    Here is a generalized Laguerre polynomial.

    In[2]:=

    Out[2]=

    This is the derivative.

    In[3]:=

    Out[3]=

    This is the integral.

    In[4]:=

    Out[4]=

    This is a series expansion around .

    In[5]:=

    Out[5]=