int gsl_sf_mathieu_Ms_array(int kind, int nmin, int nmax, double qq,
double zz, gsl_sf_mathieu_workspace *work,
double result_array[])
{
int even_odd, order, ii, kk, mm, status;
double maxerr = 1e-14, amax, pi = M_PI, fn;
double coeff[GSL_SF_MATHIEU_COEFF], fc;
double j1c, z2c, j1mc, z2mc, j1pc, z2pc;
double u1, u2;
double *bb = work->bb;
/* Initialize the result array to zeroes. */
for (ii=0; ii<nmax-nmin+1; ii++)
result_array[ii] = 0.0;
/* Check for out of bounds parameters. */
if (qq <= 0.0)
{
GSL_ERROR("q must be greater than zero", GSL_EINVAL);
}
if (kind < 1 || kind > 2)
{
GSL_ERROR("kind must be 1 or 2", GSL_EINVAL);
}
mm = 0;
amax = 0.0;
fn = 0.0;
u1 = sqrt(qq)*exp(-1.0*zz);
u2 = sqrt(qq)*exp(zz);
/* Compute all eigenvalues up to nmax. */
gsl_sf_mathieu_b_array(0, nmax, qq, work, bb);
for (ii=0, order=nmin; order<=nmax; ii++, order++)
{
even_odd = 0;
if (order % 2 != 0)
even_odd = 1;
/* Compute the series coefficients. */
status = gsl_sf_mathieu_b_coeff(order, qq, bb[order], coeff);
if (status != GSL_SUCCESS)
{
return status;
}
if (even_odd == 0)
{
for (kk=0; kk<GSL_SF_MATHIEU_COEFF; kk++)
{
amax = GSL_MAX(amax, fabs(coeff[kk]));
if (fabs(coeff[kk])/amax < maxerr)
break;
j1mc = gsl_sf_bessel_Jn(kk, u1);
j1pc = gsl_sf_bessel_Jn(kk+2, u1);
if (kind == 1)
{
z2mc = gsl_sf_bessel_Jn(kk, u2);
z2pc = gsl_sf_bessel_Jn(kk+2, u2);
}
else /* kind = 2 */
{
z2mc = gsl_sf_bessel_Yn(kk, u2);
z2pc = gsl_sf_bessel_Yn(kk+2, u2);
}
fc = pow(-1.0, 0.5*order+kk+1)*coeff[kk];
fn += fc*(j1mc*z2pc - j1pc*z2mc);
}
fn *= sqrt(pi/2.0)/coeff[0];
}
else
{
for (kk=0; kk<GSL_SF_MATHIEU_COEFF; kk++)
{
amax = GSL_MAX(amax, fabs(coeff[kk]));
if (fabs(coeff[kk])/amax < maxerr)
break;
j1c = gsl_sf_bessel_Jn(kk, u1);
j1pc = gsl_sf_bessel_Jn(kk+1, u1);
if (kind == 1)
{
z2c = gsl_sf_bessel_Jn(kk, u2);
z2pc = gsl_sf_bessel_Jn(kk+1, u2);
}
else /* kind = 2 */
{
z2c = gsl_sf_bessel_Yn(kk, u2);
z2pc = gsl_sf_bessel_Yn(kk+1, u2);
}
fc = pow(-1.0, 0.5*(order-1)+kk)*coeff[kk];
fn += fc*(j1c*z2pc - j1pc*z2c);
}
fn *= sqrt(pi/2.0)/coeff[0];
}
result_array[ii] = fn;
} /* order loop */
return GSL_SUCCESS;
}
static Real _Y(UnsignedInteger n, Real z)
{
return gsl_sf_bessel_Yn(n, z);
}
int gsl_sf_mathieu_Mc(int kind, int order, double qq, double zz,
gsl_sf_result *result)
{
int even_odd, kk, mm, status;
double maxerr = 1e-14, amax, pi = M_PI, fn, factor;
double coeff[GSL_SF_MATHIEU_COEFF], fc;
double j1c, z2c, j1pc, z2pc;
double u1, u2;
gsl_sf_result aa;
/* Check for out of bounds parameters. */
if (qq <= 0.0)
{
GSL_ERROR("q must be greater than zero", GSL_EINVAL);
}
if (kind < 1 || kind > 2)
{
GSL_ERROR("kind must be 1 or 2", GSL_EINVAL);
}
mm = 0;
amax = 0.0;
fn = 0.0;
u1 = sqrt(qq)*exp(-1.0*zz);
u2 = sqrt(qq)*exp(zz);
even_odd = 0;
if (order % 2 != 0)
even_odd = 1;
/* Compute the characteristic value. */
status = gsl_sf_mathieu_a(order, qq, &aa);
if (status != GSL_SUCCESS)
{
return status;
}
/* Compute the series coefficients. */
status = gsl_sf_mathieu_a_coeff(order, qq, aa.val, coeff);
if (status != GSL_SUCCESS)
{
return status;
}
if (even_odd == 0)
{
for (kk=0; kk<GSL_SF_MATHIEU_COEFF; kk++)
{
amax = GSL_MAX(amax, fabs(coeff[kk]));
if (fabs(coeff[kk])/amax < maxerr)
break;
j1c = gsl_sf_bessel_Jn(kk, u1);
if (kind == 1)
{
z2c = gsl_sf_bessel_Jn(kk, u2);
}
else /* kind = 2 */
{
z2c = gsl_sf_bessel_Yn(kk, u2);
}
fc = pow(-1.0, 0.5*order+kk)*coeff[kk];
fn += fc*j1c*z2c;
}
fn *= sqrt(pi/2.0)/coeff[0];
}
else
{
for (kk=0; kk<GSL_SF_MATHIEU_COEFF; kk++)
{
amax = GSL_MAX(amax, fabs(coeff[kk]));
if (fabs(coeff[kk])/amax < maxerr)
break;
j1c = gsl_sf_bessel_Jn(kk, u1);
j1pc = gsl_sf_bessel_Jn(kk+1, u1);
if (kind == 1)
{
z2c = gsl_sf_bessel_Jn(kk, u2);
z2pc = gsl_sf_bessel_Jn(kk+1, u2);
}
else /* kind = 2 */
{
z2c = gsl_sf_bessel_Yn(kk, u2);
z2pc = gsl_sf_bessel_Yn(kk+1, u2);
}
fc = pow(-1.0, 0.5*(order-1)+kk)*coeff[kk];
fn += fc*(j1c*z2pc + j1pc*z2c);
}
fn *= sqrt(pi/2.0)/coeff[0];
}
result->val = fn;
result->err = 2.0*GSL_DBL_EPSILON;
factor = fabs(fn);
if (factor > 1.0)
result->err *= factor;
return GSL_SUCCESS;
}