Mathematica 9 is now available
 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]=



    Any questions about topics on this page? Click here to get an individual response.Buy NowMore Information
    THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
    SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.