boostmath (version 1.0.0)

bessel_functions: Bessel Functions, Their Derivatives, and Zeros

Description

Functions to compute Bessel functions of the first and second kind, their modified versions, spherical Bessel functions, and their derivatives and zeros.

Usage

cyl_bessel_j(v, x)
cyl_neumann(v, x)
cyl_bessel_j_zero(v, m = NULL, start_index = NULL, number_of_zeros = NULL)
cyl_neumann_zero(v, m = NULL, start_index = NULL, number_of_zeros = NULL)
cyl_bessel_i(v, x)
cyl_bessel_k(v, x)
sph_bessel(v, x)
sph_neumann(v, x)
cyl_bessel_j_prime(v, x)
cyl_neumann_prime(v, x)
cyl_bessel_i_prime(v, x)
cyl_bessel_k_prime(v, x)
sph_bessel_prime(v, x)
sph_neumann_prime(v, x)

Value

Single numeric value for the Bessel functions and their derivatives, or a vector of length number_of_zeros for the multiple zero functions.

Arguments

v

Order of the Bessel function

x

Argument of the Bessel function

m

The index of the zero to find (1-based).

start_index

The starting index for the zeros (1-based).

number_of_zeros

The number of zeros to find.

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Bessel function of the first kind J_0(1)
cyl_bessel_j(0, 1)
# Bessel function of the second kind Y_0(1)
cyl_neumann(0, 1)
# Modified Bessel function of the first kind I_0(1)
cyl_bessel_i(0, 1)
# Modified Bessel function of the second kind K_0(1)
cyl_bessel_k(0, 1)
# Spherical Bessel function of the first kind j_0(1)
sph_bessel(0, 1)
# Spherical Bessel function of the second kind y_0(1)
sph_neumann(0, 1)
# Derivative of the Bessel function of the first kind J_0(1)
cyl_bessel_j_prime(0, 1)
# Derivative of the Bessel function of the second kind Y_0(1)
cyl_neumann_prime(0, 1)
# Derivative of the modified Bessel function of the first kind I_0(1)
cyl_bessel_i_prime(0, 1)
# Derivative of the modified Bessel function of the second kind K_0(1)
cyl_bessel_k_prime(0, 1)
# Derivative of the spherical Bessel function of the first kind j_0(1)
sph_bessel_prime(0, 1)
# Derivative of the spherical Bessel function of the second kind y_0(1)
sph_neumann_prime(0, 1)
# Finding the first zero of the Bessel function of the first kind J_0
cyl_bessel_j_zero(0, 1)
# Finding the first zero of the Bessel function of the second kind Y_0
cyl_neumann_zero(0, 1)
# Finding multiple zeros of the Bessel function of the first kind J_0 starting from index 1
cyl_bessel_j_zero(0, start_index = 1, number_of_zeros = 5)
# Finding multiple zeros of the Bessel function of the second kind Y_0 starting from index 1
cyl_neumann_zero(0, start_index = 1, number_of_zeros = 5)