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.  The functions described in this section are declared in the header file gsl_sf_coupling.h.

3-j Symbols
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 -- Function: double gsl_sf_coupling_3j (int TWO_JA, int TWO_JB, int TWO_JC, int TWO_MA, int TWO_MB, int TWO_MC)
 -- Function: int gsl_sf_coupling_3j_e (int TWO_JA, int TWO_JB, int TWO_JC, int TWO_MA, int TWO_MB, int TWO_MC, gsl_sf_result * RESULT)
     These routines compute the Wigner 3-j coefficient,

          (ja jb jc
           ma mb mc)

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

6-j Symbols
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 -- Function: double gsl_sf_coupling_6j (int TWO_JA, int TWO_JB, int TWO_JC, int TWO_JD, int TWO_JE, int TWO_JF)
 -- Function: int gsl_sf_coupling_6j_e (int TWO_JA, int TWO_JB, int TWO_JC, int TWO_JD, int TWO_JE, int TWO_JF, gsl_sf_result * RESULT)
     These routines compute the Wigner 6-j coefficient,

          {ja jb jc
           jd je jf}

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

9-j Symbols
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 -- Function: double gsl_sf_coupling_9j (int TWO_JA, int TWO_JB, int TWO_JC, int TWO_JD, int TWO_JE, int TWO_JF, int TWO_JG, int TWO_JH, int TWO_JI)
 -- Function: int gsl_sf_coupling_9j_e (int TWO_JA, int TWO_JB, int TWO_JC, int TWO_JD, int TWO_JE, int TWO_JF, int TWO_JG, int TWO_JH, int TWO_JI, gsl_sf_result * RESULT)
     These routines compute the Wigner 9-j coefficient,

          {ja jb jc
           jd je jf
           jg jh ji}

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