


Coupling Coefficients
=====================

The Wigner 3-j, 6-j and 9-j symbols give the coupling coefficients
for combined angular momentum vectors. Since the arguments of the
standard coupling coefficient functions are integer or half-integer,
the arguments of the following functions are, by convention,
integers equal to twice the actual spin value. For information on
the 3-j coefficients see Abramowitz & Stegun, Section 27.9.

.. index:: coupling coefficient

.. function:: gsl_sf_coupling_3j(two_ja, two_jb, two_jc, two_ma, two_mb, two_mc)

 These routines compute the Wigner 3-j coefficient,

 .. math::
   \left( \begin{array}{ccc}
          ja & jb & jc \\
          ma & mb & mc
          \end{array} \right)

 where the arguments are given in half-integer units, ja = two_ja / 2,
 ma = two_ma / 2, etc.

.. index:: Wigner 3-j coefficient

.. function::
  gsl_sf_coupling_6j(two_ja, two_jb, two_jc, two_jd, two_je, two_jf)

 These routines compute the Wigner 6-j coefficient,

 .. math::
   \left( \begin{array}{ccc}
          ja & jb & jc \\
          jd & je & jf
          \end{array} \right)

 where the arguments are given in half-integer units, ja = two_ja / 2,
 jb = two_jb / 2, etc.

.. index:: Wigner 6-j coefficient

.. function::
  gsl_sf_coupling_9j(two_ja, two_jb, two_jc, two_jd, two_je, two_jf, two_jg, two_jh, two_ji)

 These routines compute the Wigner 9-j coefficient,

 .. math::
   \left( \begin{array}{ccc}
          ja & jb & jc \\
          jd & je & jf \\
          jg & jh & ji
          \end{array} \right)

 where the arguments are given in half-integer units, ja = two_ja / 2,
 jb = two_jb / 2, etc.

.. index:: Wigner 9-j coefficient
