MATLAB Function Reference |
Modified Bessel function of the second kind
Syntax
Definitions
where is a real constant, is called the modified Bessel's equation, and its solutions are known as modified Bessel functions.
A solution of the second kind can be expressed as
where and form a fundamental set of solutions of the modified Bessel's equation for noninteger
and is the gamma function. is independent of .
can be computed using besseli
.
Description
K = besselk(nu,Z)
computes the modified Bessel function of the second kind, , for each element of the array Z
. The order nu
need not be an integer, but must be real. The argument Z
can be complex. The result is real where Z
is positive.
If nu
and Z
are arrays of the same size, the result is also that size. If either input is a scalar, it is expanded to the other input's size. If one input is a row vector and the other is a column vector, the result is a two-dimensional table of function values.
K = besselk(nu,Z,1)
computes besselk(nu,Z).*exp(Z)
.
[K,ierr] = besselk(...)
also returns completion flags in an array the same size as K
.
Examples
format long z = (0:0.2:1)'; besselk(1,z) ans = Inf 4.77597254322047 2.18435442473269 1.30283493976350 0.86178163447218 0.60190723019723
Example 2. besselk(3:9,(0:.2:10)',1)
generates part of the table on page 424 of [1] Abramowitz and Stegun, Handbook of Mathematical Functions.
Algorithm
The besselk
function uses a Fortran MEX-file to call a library developed by D. E. Amos [3] [4].
See Also
airy
, besselh
, besseli
, besselj
, bessely
References
[1] Abramowitz, M. and I.A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series #55, Dover Publications, 1965, sections 9.1.1, 9.1.89 and 9.12, formulas 9.1.10 and 9.2.5.
[2] Carrier, Krook, and Pearson, Functions of a Complex Variable: Theory and Technique, Hod Books, 1983, section 5.5.
[3] Amos, D. E., "A Subroutine Package for Bessel Functions of a Complex Argument and Nonnegative Order," Sandia National Laboratory Report, SAND85-1018, May, 1985.
[4] Amos, D. E., "A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order," Trans. Math. Software, 1986.
besselj | bessely |
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