Module rgsl::bessel
[−]
[src]
Functions
| I0 |
This routine computes the regular modified cylindrical Bessel function of zeroth order, I_0(x) |
| I0_e |
This routine computes the regular modified cylindrical Bessel function of zeroth order, I_0(x) |
| I0_scaled |
This routine computes the scaled regular modified cylindrical Bessel function of zeroth order \exp(-|x|) I_0(x). |
| I0_scaled_e |
This routine computes the scaled regular modified cylindrical Bessel function of zeroth order \exp(-|x|) I_0(x). |
| I1 |
This routine computes the regular modified cylindrical Bessel function of first order, I_1(x). |
| I1_e |
This routine computes the regular modified cylindrical Bessel function of first order, I_1(x). |
| I1_scaled |
This routine computes the scaled regular modified cylindrical Bessel function of first order \exp(-|x|) I_1(x). |
| I1_scaled_e |
This routine computes the scaled regular modified cylindrical Bessel function of first order \exp(-|x|) I_1(x). |
| In |
This routine computes the regular modified cylindrical Bessel function of order n, I_n(x). |
| In_array |
This routine computes the values of the regular modified cylindrical Bessel functions I_n(x) for n from nmin to nmax inclusive, storing the results in the array result_array. The start of the range nmin must be positive or zero. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. |
| In_e |
This routine computes the regular modified cylindrical Bessel function of order n, I_n(x). |
| In_scaled |
This routine computes the scaled regular modified cylindrical Bessel function of order n, \exp(-|x|) I_n(x) |
| In_scaled_array |
This routine computes the values of the scaled regular cylindrical Bessel functions \exp(-|x|) I_n(x) for n from nmin to nmax inclusive, storing the results in the array result_array. The start of the range nmin must be positive or zero. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. |
| In_scaled_e |
This routine computes the scaled regular modified cylindrical Bessel function of order n, \exp(-|x|) I_n(x) |
| Inu |
This routine computes the regular modified Bessel function of fractional order \nu, I_\nu(x) for x>0, \nu>0. |
| Inu_e |
This routine computes the regular modified Bessel function of fractional order \nu, I_\nu(x) for x>0, \nu>0. |
| Inu_scaled |
This routine computes the scaled regular modified Bessel function of fractional order \nu, \exp(-|x|)I_\nu(x) for x>0, \nu>0. |
| Inu_scaled_e |
This routine computes the scaled regular modified Bessel function of fractional order \nu, \exp(-|x|)I_\nu(x) for x>0, \nu>0. |
| J0 |
This routine computes the regular cylindrical Bessel function of zeroth order, J_0(x). |
| J0_e |
This routine computes the regular cylindrical Bessel function of zeroth order, J_0(x). |
| J1 |
This routine computes the regular cylindrical Bessel function of first order, J_1(x). |
| J1_e |
This routine computes the regular cylindrical Bessel function of first order, J_1(x). |
| Jn |
This routine computes the regular cylindrical Bessel function of order n, J_n(x). |
| Jn_array |
This routine computes the values of the regular cylindrical Bessel functions J_n(x) for n from nmin to nmax inclusive, storing the results in the array result_array. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. |
| Jn_e |
This routine computes the regular cylindrical Bessel function of order n, J_n(x). |
| Jnu |
This routine computes the regular cylindrical Bessel function of fractional order \nu, J_\nu(x). |
| Jnu_e |
This routine computes the regular cylindrical Bessel function of fractional order \nu, J_\nu(x). |
| K0 |
This routine computes the irregular modified cylindrical Bessel function of zeroth order, K_0(x), for x > 0. |
| K0_e |
This routine computes the irregular modified cylindrical Bessel function of zeroth order, K_0(x), for x > 0. |
| K0_scaled |
This routine computes the scaled irregular modified cylindrical Bessel function of zeroth order \exp(x) K_0(x) for x>0. |
| K0_scaled_e |
This routine computes the scaled irregular modified cylindrical Bessel function of zeroth order \exp(x) K_0(x) for x>0. |
| K1 |
This routine computes the irregular modified cylindrical Bessel function of first order, K_1(x), for x > 0. |
| K1_e |
This routine computes the irregular modified cylindrical Bessel function of first order, K_1(x), for x > 0. |
| K1_scaled |
This routine computes the scaled irregular modified cylindrical Bessel function of first order \exp(x) K_1(x) for x>0. |
| K1_scaled_e |
This routine computes the scaled irregular modified cylindrical Bessel function of first order \exp(x) K_1(x) for x>0. |
| Kn |
This routine computes the irregular modified cylindrical Bessel function of order n, K_n(x), for x > 0. |
| Kn_array |
This routine computes the values of the irregular modified cylindrical Bessel functions K_n(x) for n from nmin to nmax inclusive, storing the results in the array result_array. The start of the range nmin must be positive or zero. The domain of the function is x>0. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. |
| Kn_e |
This routine computes the irregular modified cylindrical Bessel function of order n, K_n(x), for x > 0. |
| Kn_scaled |
This routine computes the scaled irregular modified cylindrical Bessel function of order n, \exp(x) K_n(x), for x>0. |
| Kn_scaled_array |
This routine computes the values of the scaled irregular cylindrical Bessel functions \exp(x) K_n(x) for n from nmin to nmax inclusive, storing the results in the array result_array. The start of the range nmin must be positive or zero. The domain of the function is x>0. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. |
| Kn_scaled_e |
This routine computes the scaled irregular modified cylindrical Bessel function of order n, \exp(x) K_n(x), for x>0. |
| Knu |
This routine computes the irregular modified Bessel function of fractional order \nu, K_\nu(x) for x>0, \nu>0. |
| Knu_e |
This routine computes the irregular modified Bessel function of fractional order \nu, K_\nu(x) for x>0, \nu>0. |
| Knu_scaled |
This routine computes the scaled irregular modified Bessel function of fractional order \nu, \exp(+|x|) K_\nu(x) for x>0, \nu>0. |
| Knu_scaled_e |
This routine computes the scaled irregular modified Bessel function of fractional order \nu, \exp(+|x|) K_\nu(x) for x>0, \nu>0. |
| Y0 |
This routine computes the irregular cylindrical Bessel function of zeroth order, Y_0(x), for x>0. |
| Y0_e |
This routine computes the irregular cylindrical Bessel function of zeroth order, Y_0(x), for x>0. |
| Y1 |
This routine computes the irregular cylindrical Bessel function of first order, Y_1(x), for x>0. |
| Y1_e |
This routine computes the irregular cylindrical Bessel function of first order, Y_1(x), for x>0. |
| Yn |
This routine computes the irregular cylindrical Bessel function of order n, Y_n(x), for x>0. |
| Yn_array |
This routine computes the values of the irregular cylindrical Bessel functions Y_n(x) for n from nmin to nmax inclusive, storing the results in the array result_array. The domain of the function is x>0. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. |
| Yn_e |
This routine computes the irregular cylindrical Bessel function of order n, Y_n(x), for x>0. |
| Ynu |
This routine computes the irregular cylindrical Bessel function of fractional order \nu, Y_\nu(x). |
| Ynu_e |
This routine computes the irregular cylindrical Bessel function of fractional order \nu, Y_\nu(x). |
| i0_scaled |
This routine computes the scaled regular modified spherical Bessel function of zeroth order, \exp(-|x|) i_0(x). |
| i0_scaled_e |
This routine computes the scaled regular modified spherical Bessel function of zeroth order, \exp(-|x|) i_0(x). |
| i1_scaled |
This routine computes the scaled regular modified spherical Bessel function of first order, \exp(-|x|) i_1(x). |
| i1_scaled_e |
This routine computes the scaled regular modified spherical Bessel function of first order, \exp(-|x|) i_1(x). |
| i2_scaled |
This routine computes the scaled regular modified spherical Bessel function of second order, \exp(-|x|) i_2(x) |
| i2_scaled_e |
This routine computes the scaled regular modified spherical Bessel function of second order, \exp(-|x|) i_2(x) |
| il_scaled |
This routine computes the scaled regular modified spherical Bessel function of order l, \exp(-|x|) i_l(x) |
| il_scaled_array |
This routine computes the values of the scaled regular modified cylindrical Bessel functions \exp(-|x|) i_l(x) for l from 0 to lmax inclusive for lmax >= 0, storing the results in the array result_array. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. |
| il_scaled_e |
This routine computes the scaled regular modified spherical Bessel function of order l, \exp(-|x|) i_l(x) |
| j0 |
This routine computes the regular spherical Bessel function of zeroth order, j_0(x) = \sin(x)/x. |
| j0_e |
This routine computes the regular spherical Bessel function of zeroth order, j_0(x) = \sin(x)/x. |
| j1 |
This routine computes the regular spherical Bessel function of first order, j_1(x) = (\sin(x)/x - \cos(x))/x. |
| j1_e |
This routine computes the regular spherical Bessel function of first order, j_1(x) = (\sin(x)/x - \cos(x))/x. |
| j2 |
This routine computes the regular spherical Bessel function of second order, j_2(x) = ((3/x2 - 1)\sin(x) - 3\cos(x)/x)/x. |
| j2_e |
This routine computes the regular spherical Bessel function of second order, j_2(x) = ((3/x2 - 1)\sin(x) - 3\cos(x)/x)/x. |
| jl |
This routine computes the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0. |
| jl_array |
This routine computes the values of the regular spherical Bessel functions j_l(x) for l from 0 to lmax inclusive for lmax >= 0 and x >= 0, storing the results in the array result_array. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. |
| jl_e |
This routine computes the regular spherical Bessel function of order l, j_l(x), for l >= 0 and x >= 0. |
| jl_steed_array |
This routine uses Steed’s method to compute the values of the regular spherical Bessel functions j_l(x) for l from 0 to lmax inclusive for lmax >= 0 and x >= 0, storing the results in the array result_array. The Steed/Barnett algorithm is described in Comp. Phys. Comm. 21, 297 (1981). Steed’s method is more stable than the recurrence used in the other functions but is also slower. |
| k0_scaled |
The irregular modified spherical Bessel functions k_l(x) are related to the irregular modified Bessel functions of fractional order, k_l(x) = \sqrt{\pi/(2x)} K_{l+1/2}(x). This routine computes the scaled irregular modified spherical Bessel function of zeroth order, \exp(x) k_0(x), for x>0. |
| k0_scaled_e |
The irregular modified spherical Bessel functions k_l(x) are related to the irregular modified Bessel functions of fractional order, k_l(x) = \sqrt{\pi/(2x)} K_{l+1/2}(x). This routine computes the scaled irregular modified spherical Bessel function of zeroth order, \exp(x) k_0(x), for x>0. |
| k1_scaled |
This routine computes the scaled irregular modified spherical Bessel function of first order, \exp(x) k_1(x), for x>0. |
| k1_scaled_e |
This routine computes the scaled irregular modified spherical Bessel function of first order, \exp(x) k_1(x), for x>0. |
| k2_scaled |
This routine computes the scaled irregular modified spherical Bessel function of second order, \exp(x) k_2(x), for x>0. |
| k2_scaled_e |
This routine computes the scaled irregular modified spherical Bessel function of second order, \exp(x) k_2(x), for x>0. |
| kl_scaled |
This routine computes the scaled irregular modified spherical Bessel function of order l, \exp(x) k_l(x), for x>0. |
| kl_scaled_array |
This routine computes the values of the scaled irregular modified spherical Bessel functions \exp(x) k_l(x) for l from 0 to lmax inclusive for lmax >= 0 and x>0, storing the results in the array result_array. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. |
| kl_scaled_e |
This routine computes the scaled irregular modified spherical Bessel function of order l, \exp(x) k_l(x), for x>0. |
| lnKnu |
This routine computes the logarithm of the irregular modified Bessel function of fractional order \nu, \ln(K_\nu(x)) for x>0, \nu>0. |
| lnKnu_e |
This routine computes the logarithm of the irregular modified Bessel function of fractional order \nu, \ln(K_\nu(x)) for x>0, \nu>0. |
| sequence_Jnu |
This function computes the regular cylindrical Bessel function of fractional order \nu, J_\nu(x), evaluated at a series of x values. The array v of length size 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). |
| y0 |
This routine computes the irregular spherical Bessel function of zeroth order, y_0(x) = -\cos(x)/x. |
| y0_e |
This routine computes the irregular spherical Bessel function of zeroth order, y_0(x) = -\cos(x)/x. |
| y1 |
This routine computes the irregular spherical Bessel function of first order, y_1(x) = -(\cos(x)/x + \sin(x))/x. |
| y1_e |
This routine computes the irregular spherical Bessel function of first order, y_1(x) = -(\cos(x)/x + \sin(x))/x. |
| y2 |
This routine computes the irregular spherical Bessel function of second order, y_2(x) = (-3/x3 + 1/x)\cos(x) - (3/x2)\sin(x). |
| y2_e |
This routine computes the irregular spherical Bessel function of second order, y_2(x) = (-3/x3 + 1/x)\cos(x) - (3/x2)\sin(x). |
| yl |
This routine computes the irregular spherical Bessel function of order l, y_l(x), for l >= 0. |
| yl_array |
This routine computes the values of the irregular spherical Bessel functions y_l(x) for l from 0 to lmax inclusive for lmax >= 0, storing the results in the array result_array. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. |
| yl_e |
This routine computes the irregular spherical Bessel function of order l, y_l(x), for l >= 0. |
| zero_J0 |
This routine computes the location of the s-th positive zero of the Bessel function J_0(x). |
| zero_J0_e |
This routine computes the location of the s-th positive zero of the Bessel function J_0(x). |
| zero_J1 |
This routine computes the location of the s-th positive zero of the Bessel function J_1(x). |
| zero_J1_e |
This routine computes the location of the s-th positive zero of the Bessel function J_1(x). |
| zero_Jnu |
This routine computes the location of the s-th positive zero of the Bessel function J_\nu(x). The current implementation does not support negative values of nu. |
| zero_Jnu_e |
This routine computes the location of the s-th positive zero of the Bessel function J_\nu(x). The current implementation does not support negative values of nu. |