besselk

Purpose

Computes the modified Bessel function of the second kind, \(K_n(x)\).

Format

besselk(n, x)

Parameters:

• n (scalar or matrix) – order. Currently only integer orders are supported.

• x (scalar or matrix ExE) – conformable with n. x must be greater than 0.

Returns:

K (scalar or matrix) – the modified Bessel function result.

Examples

Basic usage

x = { 0,
    0.5,
      1,
    1.5,
      2 };

K = besselk(1, x);

After the above code, K, should equal:

+INF
1.6564411
0.60190723
0.27738780
0.13986588

Compute data for first 3 orders

// Row vector of orders, 'n'
n = { 0 1 2 };

// Column vector 'x'
x = { 0,
    0.5,
      1,
    1.5,
      2 };

// Compute function for each order, 'n', at all 'x' points
K = besselk(n, x);

After the code above, K should equal:

+INF             +INF             +INF
0.92441907       1.6564411        7.5501836
0.42102444       0.60190723       1.6248389
0.21380556       0.27738780       0.58365596
0.11389387       0.13986588       0.25375975

Remarks

Currently the algorithm has the following limitations:

• The order, n, must be an integer.

• The values of x must be positive.

• The maximum supported value for x with an order greater than 1 is limited to approximately 740. If the input is out of range, a NaN (missing value) will be returned. If necessary, use the function ismiss() to check for NaN’s in the output.

See also

Functions bessely(), mbesseli(), besselj()