GSL::Sf::bessel_J0(x)
-
Computes the regular cylindrical Bessel function of zeroth order, J_0(x).
GSL::Sf::bessel_J1(x)
-
Computes the regular cylindrical Bessel function of first order, J_1(x).
GSL::Sf::bessel_Jn(n, x)
-
Computes the regular cylindrical Bessel function of order n, J_n(x).
GSL::Sf::bessel_Jn_array(nmin, nmax, x)
-
Computes the values of the regular cylindrical Bessel functions J_n(x)
for n from nmin to nmax inclusive, and returns the
results as a
GSL::Vector
object.
The values are computed using recurrence relations, for efficiency,
and therefore may differ slightly from the exact values.
GSL::Sf::bessel_Y0(x)
-
Computes the irregular cylindrical Bessel function of zeroth order, Y_0(x).
GSL::Sf::bessel_Y1(x)
-
Computes the irregular cylindrical Bessel function of first order, Y_1(x).
GSL::Sf::bessel_Yn(n, x)
-
Computes the irregular cylindrical Bessel function of order n, Y_n(x).
GSL::Sf::bessel_Yn_array(nmin, nmax, x)
-
Computes the values of the irregular cylindrical Bessel functions Y_n(x)
for n from nmin to nmax inclusive, and returns the
results as a
GSL::Vector
object.
The values are computed using recurrence relations, for efficiency,
and therefore may differ slightly from the exact values.
GSL::Sf::bessel_I0(x)
-
Computes the regular modified cylindrical Bessel function of zeroth order,
I_0(x).
GSL::Sf::bessel_I1(x)
-
Computes the regular modified cylindrical Bessel function of first order,
I_1(x).
GSL::Sf::bessel_In(n, x)
-
Computes the regular modified cylindrical Bessel function of order n,
I_n(x).
GSL::Sf::bessel_In_array(nmin, nmax, x)
-
Computes the values of the regular modified cylindrical Bessel functions
I_n(x) for n from nmin to nmax inclusive, and returns the
results as a
GSL::Vector
object. 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.
GSL::Sf::bessel_I0_scaled(x)
-
Computes the scaled regular modified cylindrical Bessel function of
zeroth order, exp(-|x|) I_0(x).
GSL::Sf::bessel_I1_scaled(x)
-
Computes the scaled regular modified cylindrical Bessel function of first
order, exp(-|x|)I_1(x).
GSL::Sf::bessel_In_scaled(n, x)
-
Computes the scaled regular modified cylindrical Bessel function of order
n, exp(-|x|) I_n(x).
GSL::Sf::bessel_In_scaled_array(nmin, nmax, x)
-
Computes the values of the scaled regular modified cylindrical Bessel
functions exp(-|x|) I_n(x) for n from nmin to nmax inclusive,
and returns the results as a
GSL::Vector
object. 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.
GSL::Sf::bessel_K0(x)
-
Computes the irregular modified cylindrical Bessel function
of zeroth order, K_0(x), for x > 0.
GSL::Sf::bessel_K1(x)
-
Computes the irregular modified cylindrical Bessel function
of first order, K_1(x), for x > 0.
GSL::Sf::bessel_Kn(n, x)
-
Computes the irregular modified cylindrical Bessel function
of order n, K_n(x), for x > 0.
GSL::Sf::bessel_Kn_array(nmin, nmax, x)
-
Computes the values of the irregular modified cylindrical Bessel
functions K_n(x) for n from nmin to nmax inclusive,
and returns the results as a
GSL::Vector
object.
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.
GSL::Sf::bessel_K0_scaled(x)
-
Computes the scaled irregular modified cylindrical Bessel function
of zeroth order exp(x) K_0(x) for x>0.
GSL::Sf::bessel_K1_scaled(x)
-
Computes the scaled irregular modified cylindrical Bessel function
of first order exp(x) K_1(x) for x>0
GSL::Sf::bessel_Kn_scaled(n, x)
-
Computes the scaled irregular modified cylindrical Bessel function
of order n, exp(x) K_n(x), for x>0.
GSL::Sf::bessel_Kn_scaled_array(nmin, nmax, x)
-
Computes the values of the scaled irregular cylindrical Bessel functions
exp(x) K_n(x) for n from nmin to nmax inclusive,
and returns the results as a
GSL::Vector
object.
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.
GSL::Sf::bessel_j0(x)
-
Computes the regular spherical Bessel function of zeroth order,
j0(x) = sin(x)/x.
GSL::Sf::bessel_j1(x)
-
Computes the regular spherical Bessel function of first order,
j1(x) = (sin(x)/x - cos(x))/x.
GSL::Sf::bessel_j2(x)
-
Computes the regular spherical Bessel function of second order,
j2(x) = ((3/x^2 - 1)sin(x) - 3cos(x)/x)/x.
GSL::Sf::bessel_jl(l, x)
-
Computes the regular spherical Bessel function of order l,
j_l(x), for l >= 0 and x >= 0.
GSL::Sf::bessel_jl_array(lmax, x)
-
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,
and returns the results as a
GSL::Vector
object.
The values are computed using recurrence relations, for efficiency,
and therefore may differ slightly from the exact values.
GSL::Sf::bessel_jl_steed_array(lmax, x)
-
This method 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, and returns the results as a
GSL::Vector
object. 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.
GSL::Sf::bessel_y0(x)
-
Computes the irregular spherical Bessel function of zeroth order,
y_0(x) = -cos(x)/x.
GSL::Sf::bessel_y1(x)
-
Computes the irregular spherical Bessel function of first order,
y_1(x) = -(cos(x)/x + sin(x))/x.
GSL::Sf::bessel_y2(x)
-
Computes the irregular spherical Bessel function of second order,
y_2(x) = (-3/x^3 + 1/x)cos(x) - (3/x^2)sin(x).
GSL::Sf::bessel_yl(l, x)
-
Computes the irregular spherical Bessel function of order l,
y_l(x), for l >= 0.
GSL::Sf::bessel_yl_array(lmax, x)
-
This method computes the values of the irregular spherical Bessel functions
y_l(x) for l from 0 to lmax inclusive for lmax >= 0),
and returns the results as a
GSL::Vector
object.
The values are computed using recurrence relations, for efficiency,
and therefore may differ slightly from the exact values.
GSL::Sf::bessel_i0_scaled(x)
-
Computes the scaled regular modified spherical Bessel function of zeroth
order, exp(-|x|) i_0(x).
GSL::Sf::bessel_i1_scaled(x)
-
Computes the scaled regular modified spherical Bessel function of first
order, exp(-|x|) i_1(x).
GSL::Sf::bessel_i2_scaled(x)
-
Computes the scaled regular modified spherical Bessel function of second
order, exp(-|x|) i_2(x).
GSL::Sf::bessel_il_scaled(l, x)
-
Computes the scaled regular modified spherical Bessel function of
order l, exp(-|x|) i_l(x).
GSL::Sf::bessel_il_scaled_array(lmax, x)
-
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, and returns the results as a
GSL::Vector
object.
The values are computed using recurrence relations, for efficiency,
and therefore may differ slightly from the exact values.
GSL::Sf::bessel_k0_scaled(x)
-
Computes the scaled irregular modified spherical Bessel function of zeroth
order, exp(-|x|) k_0(x).
GSL::Sf::bessel_k1_scaled(x)
-
Computes the scaled irregular modified spherical Bessel function of first
order, exp(-|x|) k_1(x).
GSL::Sf::bessel_k2_scaled(x)
-
Computes the scaled irregular modified spherical Bessel function of second
order, exp(-|x|) k_2(x).
GSL::Sf::bessel_kl_scaled(l, x)
-
Computes the scaled irregular modified spherical Bessel function of
order l, exp(-|x|) k_l(x).
GSL::Sf::bessel_kl_scaled_array(lmax, x)
-
This routine computes the values of the scaled irregular modified cylindrical
Bessel functions exp(-|x|) k_l(x) for l from 0 to lmax inclusive for
lmax >= 0, and returns the results as a
GSL::Vector
object.
The values are computed using recurrence relations, for efficiency,
and therefore may differ slightly from the exact values.
GSL::Sf::bessel_Jnu(nu, x)
-
Computes the regular cylindrical Bessel function of fractional
order nu, J_nu(x).
GSL::Sf::bessel_sequence_Jnu_e(nu, v)
GSL::Sf::bessel_sequence_Jnu_e(nu, mode, v)
-
These compute the regular cylindrical Bessel function of fractional order nu, J_nu(x),
evaluated at a series of x values. The
GSL::Vector
object v
contains the x values. They are assumed to be strictly ordered and positive.
The vector is over-written with the values of J_nu(x_i).
GSL::Sf::bessel_Ynu(nu, x)
-
Computes the irregular cylindrical Bessel function of fractional order nu,
Y_nu(x).
GSL::Sf::bessel_Inu(nu, x)
-
Computes the regular modified Bessel function of fractional order nu,
I_nu(x) for x>0, nu>0.
GSL::Sf::bessel_Inu_scaled(nu, x)
-
Computes the scaled regular modified Bessel function of fractional order nu,
exp(-|x|) I_nu(x) for x>0, nu>0.
GSL::Sf::bessel_Knu(nu, x)
-
Computes the irregular modified Bessel function of fractional order nu,
K_nu(x) for x>0, nu>0.
GSL::Sf::bessel_lnKnu(nu, x)
-
Computes the logarithm of the irregular modified Bessel function of fractional
order nu, ln(K_nu(x)) for x>0, nu>0
GSL::Sf::bessel_Knu_scaled(nu, x)
-
Computes the scaled irregular modified Bessel function of fractional order nu,
exp(+|x|) K_nu(x) for x>0, nu>0.
GSL::Sf::bessel_zero_J0(s)
-
Computes the location of the s-th positive zero of the Bessel function J_0(x).
GSL::Sf::bessel_zero_J1(s)
-
Computes the location of the s-th positive zero of the Bessel function J_1(x).
GSL::Sf::bessel_zero_Jnu(nu, s)
-
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.