Spherical Bessel functions

The spherical Bessel functions of integer order, or their derivatives, for real or complex argument, as scipy.special's spherical_jn() and siblings compute them.

Usage

sc_spherical_jn(n, z, derivative = FALSE)

sc_spherical_yn(n, z, derivative = FALSE)

sc_spherical_in(n, z, derivative = FALSE)

sc_spherical_kn(n, z, derivative = FALSE)

Arguments

n

Whole numbers within integer range, the orders.

z

Numeric or complex vector of arguments.

derivative

TRUE for the derivative with respect to z, FALSE (the default) for the function itself.

Value

A double vector, or a complex vector for complex z.

Details

• sc_spherical_jn(), sc_spherical_yn(): \(j_n(z)\) and \(y_n(z)\).

• sc_spherical_in(), sc_spherical_kn(): the modified functions \(i_n(z)\) and \(k_n(z)\).

Arguments are recycled: each must have length one or the common length. NA gives NA; NaN is evaluated as SciPy does. The result takes its dimensions, or else its names, from the arguments as base R arithmetic does, and so does each element of a list result. Conditions the kernels raise, such as a pole, are handled as sc_seterr() says.

Other packages

In gsl, for real x: bessel_jl(l, x) and bessel_yl(), and the scaled bessel_il_scaled() and bessel_kl_scaled(), which are sc_spherical_in(n, x) * exp(-abs(x)) and sc_spherical_kn(n, x) * exp(x).

See also

https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.spherical_jn.html

Examples

sc_spherical_jn(0:3, 1.5)
#> [1] 0.66499666 0.39617297 0.12734928 0.02832464
sc_spherical_jn(1, 1.5, derivative = TRUE)
#> [1] 0.136766
sc_spherical_kn(2, 1 + 1i)
#> [1] -1.415258-0.7370441i