/* Author: G. Jungman * RCS: $Id: gsl_sf_bessel.h,v 1.39 1999/04/24 17:28:34 jungman Exp $ */ #ifndef GSL_SF_BESSEL_H_ #define GSL_SF_BESSEL_H_ #include #include #include #include /* Regular Bessel Function J_0(x) * * exceptions: none */ int gsl_sf_bessel_J0_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_J0_e(double x, gsl_sf_result * result); /* Regular Bessel Function J_1(x) * * exceptions: GSL_EUNDRFLW */ int gsl_sf_bessel_J1_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_J1_e(double x, gsl_sf_result * result); /* Regular Bessel Function J_n(x) * * exceptions: GSL_EUNDRFLW */ int gsl_sf_bessel_Jn_impl(int n, double x, gsl_sf_result * result); int gsl_sf_bessel_Jn_e(int n, double x, gsl_sf_result * result); /* Regular Bessel Function J_n(x), nmin <= n <= nmax * * exceptions: GSL_EDOM, GSL_EUNDRFLW */ int gsl_sf_bessel_Jn_array_impl(int nmin, int nmax, double x, double * result_array); int gsl_sf_bessel_Jn_array_e(int nmin, int nmax, double x, double * result_array); /* Irregular Bessel function Y_0(x) * * x > 0.0 * exceptions: GSL_EDOM, GSL_EUNDRFLW */ int gsl_sf_bessel_Y0_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_Y0_e(double x, gsl_sf_result * result); /* Irregular Bessel function Y_1(x) * * x > 0.0 * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW */ int gsl_sf_bessel_Y1_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_Y1_e(double x, gsl_sf_result * result); /* Irregular Bessel function Y_n(x) * * x > 0.0 * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW */ int gsl_sf_bessel_Yn_impl(int n,double x, gsl_sf_result * result); int gsl_sf_bessel_Yn_e(int n,double x, gsl_sf_result * result); /* Irregular Bessel function Y_n(x), nmin <= n <= nmax * * x > 0.0 * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW */ int gsl_sf_bessel_Yn_array_impl(int nmin, int nmax, double x, double * result_array); int gsl_sf_bessel_Yn_array_e(int nmin, int nmax, double x, double * result_array); /* Regular modified Bessel function I_0(x) * * exceptions: GSL_EOVRFLW */ int gsl_sf_bessel_I0_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_I0_e(double x, gsl_sf_result * result); /* Regular modified Bessel function I_1(x) * * exceptions: GSL_EOVRFLW, GSL_EUNDRFLW */ int gsl_sf_bessel_I1_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_I1_e(double x, gsl_sf_result * result); /* Regular modified Bessel function I_n(x) * * exceptions: GSL_EOVRFLW, GSL_EUNDRFLW */ int gsl_sf_bessel_In_impl(int n, double x, gsl_sf_result * result); int gsl_sf_bessel_In_e(int n, double x, gsl_sf_result * result); /* Regular modified Bessel function I_n(x) for n=nmin,...,nmax * * nmin >=0, nmax >= nmin * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW */ int gsl_sf_bessel_In_array_impl(int nmin, int nmax, double x, double * result_array); int gsl_sf_bessel_In_array_e(int nmin, int nmax, double x, double * result_array); /* Scaled regular modified Bessel function * exp(-|x|) I_0(x) * * exceptions: none */ int gsl_sf_bessel_I0_scaled_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_I0_scaled_e(double x, gsl_sf_result * result); /* Scaled regular modified Bessel function * exp(-|x|) I_1(x) * * exceptions: GSL_EUNDRFLW */ int gsl_sf_bessel_I1_scaled_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_I1_scaled_e(double x, gsl_sf_result * result); /* Scaled regular modified Bessel function * exp(-|x|) I_n(x) * * exceptions: GSL_EUNDRFLW */ int gsl_sf_bessel_In_scaled_impl(int n, double x, gsl_sf_result * result); int gsl_sf_bessel_In_scaled_e(int n, double x, gsl_sf_result * result); /* Scaled regular modified Bessel function * exp(-|x|) I_n(x) for n=nmin,...,nmax * * nmin >=0, nmax >= nmin * exceptions: GSL_EUNDRFLW */ int gsl_sf_bessel_In_scaled_array_impl(int nmin, int nmax, double x, double * result_array); int gsl_sf_bessel_In_scaled_array_e(int nmin, int nmax, double x, double * result_array); /* Irregular modified Bessel function K_0(x) * * x > 0.0 * exceptions: GSL_EDOM, GSL_EUNDRFLW */ int gsl_sf_bessel_K0_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_K0_e(double x, gsl_sf_result * result); /* Irregular modified Bessel function K_1(x) * * x > 0.0 * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW */ int gsl_sf_bessel_K1_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_K1_e(double x, gsl_sf_result * result); /* Irregular modified Bessel function K_n(x) * * x > 0.0 * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW */ int gsl_sf_bessel_Kn_impl(int n, double x, gsl_sf_result * result); int gsl_sf_bessel_Kn_e(int n, double x, gsl_sf_result * result); /* Irregular modified Bessel function K_n(x) for n=nmin,...,nmax * * x > 0.0, nmin >=0, nmax >= nmin * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW */ int gsl_sf_bessel_Kn_array_impl(int nmin, int nmax, double x, double * result_array); int gsl_sf_bessel_Kn_array_e(int nmin, int nmax, double x, double * result_array); /* Scaled irregular modified Bessel function * exp(x) K_0(x) * * x > 0.0 * exceptions: GSL_EDOM */ int gsl_sf_bessel_K0_scaled_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_K0_scaled_e(double x, gsl_sf_result * result); /* Scaled irregular modified Bessel function * exp(x) K_1(x) * * x > 0.0 * exceptions: GSL_EDOM, GSL_EUNDRFLW */ int gsl_sf_bessel_K1_scaled_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_K1_scaled_e(double x, gsl_sf_result * result); /* Scaled irregular modified Bessel function * exp(x) K_n(x) * * x > 0.0 * exceptions: GSL_EDOM, GSL_EUNDRFLW */ int gsl_sf_bessel_Kn_scaled_impl(int n, double x, gsl_sf_result * result); int gsl_sf_bessel_Kn_scaled_e(int n, double x, gsl_sf_result * result); /* Scaled irregular modified Bessel function exp(x) K_n(x) for n=nmin,...,nmax * * x > 0.0, nmin >=0, nmax >= nmin * exceptions: GSL_EDOM, GSL_EUNDRFLW */ int gsl_sf_bessel_Kn_scaled_array_impl(int nmin, int nmax, double x, double * result_array); int gsl_sf_bessel_Kn_scaled_array_e(int nmin, int nmax, double x, double * result_array); /* Regular spherical Bessel function j_0(x) = sin(x)/x * * exceptions: none */ int gsl_sf_bessel_j0_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_j0_e(double x, gsl_sf_result * result); /* Regular spherical Bessel function j_1(x) = (sin(x)/x - cos(x))/x * * exceptions: GSL_EUNDRFLW */ int gsl_sf_bessel_j1_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_j1_e(double x, gsl_sf_result * result); /* Regular spherical Bessel function j_2(x) = ((3/x^2 - 1)sin(x) - 3cos(x)/x)/x * * exceptions: GSL_EUNDRFLW */ int gsl_sf_bessel_j2_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_j2_e(double x, gsl_sf_result * result); /* Regular spherical Bessel function j_l(x) * * l >= 0, x >= 0.0 * exceptions: GSL_EDOM, GSL_EUNDRFLW */ int gsl_sf_bessel_jl_impl(int l, double x, gsl_sf_result * result); int gsl_sf_bessel_jl_e(int l, double x, gsl_sf_result * result); /* Regular spherical Bessel function j_l(x) for l=0,1,...,lmax * * exceptions: GSL_EDOM, GSL_EUNDRFLW */ int gsl_sf_bessel_jl_array_impl(int lmax, double x, double * result_array); int gsl_sf_bessel_jl_array_e(int lmax, double x, double * result_array); /* Regular spherical Bessel function j_l(x) for l=0,1,...,lmax * Uses Steed's method. * * exceptions: GSL_EDOM, GSL_EUNDRFLW */ int gsl_sf_bessel_jl_steed_array_impl(int lmax, double x, double * jl_x_array); /* Irregular spherical Bessel function y_0(x) * * exceptions: none */ int gsl_sf_bessel_y0_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_y0_e(double x, gsl_sf_result * result); /* Irregular spherical Bessel function y_1(x) * * exceptions: GSL_EUNDRFLW */ int gsl_sf_bessel_y1_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_y1_e(double x, gsl_sf_result * result); /* Irregular spherical Bessel function y_2(x) * * exceptions: GSL_EUNDRFLW */ int gsl_sf_bessel_y2_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_y2_e(double x, gsl_sf_result * result); /* Irregular spherical Bessel function y_l(x) * * exceptions: GSL_EUNDRFLW */ int gsl_sf_bessel_yl_impl(int l, double x, gsl_sf_result * result); int gsl_sf_bessel_yl_e(int l, double x, gsl_sf_result * result); /* Irregular spherical Bessel function y_l(x) for l=0,1,...,lmax * * exceptions: GSL_EUNDRFLW */ int gsl_sf_bessel_yl_array_impl(int lmax, double x, double * result_array); int gsl_sf_bessel_yl_array_e(int lmax, double x, double * result_array); /* Regular scaled modified spherical Bessel function * * Exp[-|x|] i_0(x) * * exceptions: none */ int gsl_sf_bessel_i0_scaled_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_i0_scaled_e(double x, gsl_sf_result * result); /* Regular scaled modified spherical Bessel function * * Exp[-|x|] i_1(x) * * exceptions: GSL_EUNDRFLW */ int gsl_sf_bessel_i1_scaled_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_i1_scaled_e(double x, gsl_sf_result * result); /* Regular scaled modified spherical Bessel function * * Exp[-|x|] i_2(x) * * exceptions: GSL_EUNDRFLW */ int gsl_sf_bessel_i2_scaled_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_i2_scaled_e(double x, gsl_sf_result * result); /* Regular scaled modified spherical Bessel functions * * Exp[-|x|] i_l(x) * * i_l(x) = Sqrt[Pi/(2x)] BesselI[l+1/2,x] * * l >= 0 * exceptions: GSL_EDOM, GSL_EUNDRFLW */ int gsl_sf_bessel_il_scaled_impl(int l, double x, gsl_sf_result * result); int gsl_sf_bessel_il_scaled_e(int l, double x, gsl_sf_result * result); /* Regular scaled modified spherical Bessel functions * * Exp[-|x|] i_l(x) * for l=0,1,...,lmax * * exceptions: GSL_EUNDRFLW */ int gsl_sf_bessel_il_scaled_array_impl(int lmax, double x, double * result_array); int gsl_sf_bessel_il_scaled_array_e(int lmax, double x, double * result_array); /* Irregular scaled modified spherical Bessel function * Exp[x] k_0(x) * * x > 0.0 * exceptions: GSL_EDOM, GSL_EUNDRFLW */ int gsl_sf_bessel_k0_scaled_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_k0_scaled_e(double x, gsl_sf_result * result); /* Irregular modified spherical Bessel function * Exp[x] k_1(x) * * x > 0.0 * exceptions: GSL_EDOM, GSL_EUNDRFLW, GSL_EOVRFLW */ int gsl_sf_bessel_k1_scaled_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_k1_scaled_e(double x, gsl_sf_result * result); /* Irregular modified spherical Bessel function * Exp[x] k_2(x) * * x > 0.0 * exceptions: GSL_EDOM, GSL_EUNDRFLW, GSL_EOVRFLW */ int gsl_sf_bessel_k2_scaled_impl(double x, gsl_sf_result * result); int gsl_sf_bessel_k2_scaled_e(double x, gsl_sf_result * result); /* Irregular modified spherical Bessel function * Exp[x] k_l[x] * * k_l(x) = Sqrt[Pi/(2x)] BesselK[l+1/2,x] * * exceptions: GSL_EDOM, GSL_EUNDRFLW */ int gsl_sf_bessel_kl_scaled_impl(int l, double x, gsl_sf_result * result); int gsl_sf_bessel_kl_scaled_e(int l, double x, gsl_sf_result * result); /* Irregular scaled modified spherical Bessel function * Exp[x] k_l(x) * * for l=0,1,...,lmax * exceptions: GSL_EDOM, GSL_EUNDRFLW */ int gsl_sf_bessel_kl_scaled_array_impl(int lmax, double x, double * result_array); int gsl_sf_bessel_kl_scaled_array_e(int lmax, double x, double * result_array); /* Regular cylindrical Bessel function J_nu(x) * * exceptions: GSL_EDOM, GSL_EUNDRFLW */ int gsl_sf_bessel_Jnu_impl(double nu, double x, gsl_sf_result * result); int gsl_sf_bessel_Jnu_e(double nu, double x, gsl_sf_result * result); /* Irregular cylindrical Bessel function Y_nu(x) * * exceptions: */ int gsl_sf_bessel_Ynu_impl(double nu, double x, gsl_sf_result * result); int gsl_sf_bessel_Ynu_e(double nu, double x, gsl_sf_result * result); /* Regular cylindrical Bessel function J_nu(x) * evaluated at a series of x values. The array * contains the x values. They are assumed to be * strictly ordered and positive. The array is * over-written with the values of J_nu(x_i). * * exceptions: GSL_EDOM, GSL_EINVAL */ int gsl_sf_bessel_sequence_Jnu_impl(double nu, gsl_mode_t mode, size_t size, double * v); int gsl_sf_bessel_sequence_Jnu_e(double nu, gsl_mode_t mode, size_t size, double * v); /* Scaled modified cylindrical Bessel functions * * Exp[-|x|] BesselI[nu, x] * x >= 0, nu >= 0 * * exceptions: GSL_EDOM */ int gsl_sf_bessel_Inu_scaled_impl(double nu, double x, gsl_sf_result * result); int gsl_sf_bessel_Inu_scaled_e(double nu, double x, gsl_sf_result * result); /* Modified cylindrical Bessel functions * * BesselI[nu, x] * x >= 0, nu >= 0 * * exceptions: GSL_EDOM, GSL_EOVRFLW */ int gsl_sf_bessel_Inu_impl(double nu, double x, gsl_sf_result * result); int gsl_sf_bessel_Inu_e(double nu, double x, gsl_sf_result * result); /* Scaled modified cylindrical Bessel functions * * Exp[+|x|] BesselK[nu, x] * x > 0, nu >= 0 * * exceptions: GSL_EDOM */ int gsl_sf_bessel_Knu_scaled_impl(double nu, double x, gsl_sf_result * result); int gsl_sf_bessel_Knu_scaled_e(double nu, double x, gsl_sf_result * result); /* Modified cylindrical Bessel functions * * BesselK[nu, x] * x > 0, nu >= 0 * * exceptions: GSL_EDOM, GSL_EUNDRFLW */ int gsl_sf_bessel_Knu_impl(double nu, double x, gsl_sf_result * result); int gsl_sf_bessel_Knu_e(double nu, double x, gsl_sf_result * result); /* Logarithm of modified cylindrical Bessel functions. * * Log[BesselK[nu, x]] * x > 0, nu >= 0 * * exceptions: GSL_EDOM */ int gsl_sf_bessel_lnKnu_impl(double nu, double x, gsl_sf_result * result); int gsl_sf_bessel_lnKnu_e(double nu, double x, gsl_sf_result * result); /* s'th positive zero of the Bessel function J_0(x). * * exceptions: */ int gsl_sf_bessel_zero_J0_impl(int s, gsl_sf_result * result); int gsl_sf_bessel_zero_J0_e(int s, gsl_sf_result * result); /* s'th positive zero of the Bessel function J_1(x). * * exceptions: */ int gsl_sf_bessel_zero_J1_impl(int s, gsl_sf_result * result); int gsl_sf_bessel_zero_J1_e(int s, gsl_sf_result * result); /* s'th positive zero of the Bessel function J_nu(x). * * exceptions: */ int gsl_sf_bessel_zero_Jnu_impl(double nu, int s, gsl_sf_result * result); int gsl_sf_bessel_zero_Jnu_e(double nu, int s, gsl_sf_result * result); #endif /* !GSL_SF_BESSEL_H_ */