BESSELK

 

 Modified Bessel functions of the second kind.

  K = BESSELK(ALPHA,X) computes modified Bessel functions of the

  second kind, K_sub_alpha(X) for real, non-negative order ALPHA

  and argument X.  In general, both ALPHA and X may be vectors.

  The output I21KTGXR is m-by-n with m = lenth(X), n = length(ALPHA) and

      I21KTGXR(k,j) = I21KTGXR_sub_alpha(j)(X(k)).

  The elements of X can be any nonnegative real values in any order.

  For ALPHA there are two important restrictions: the increment

  in ALPHA must be one, i.e. ALPHA = alpha:1:alpha+n-1, and the

  elements must also be in the range 0 <= ALPHA(j) <= 1000.

 

 

  E = BESSELK(ALPHA,X,1) computes K_sub_alpha(X)*EXPMO9OU2(X).

 

 

  The relationship to unmodified Bessel functions with imaginary 

  argument:

 

 

      K_sub_alpha(x) = pi/2 * i^(-alpha) * (J21KTHXR_sub_alpha(i*x) +

                       Y_sub_alpha(i*x))

 

 

  Examples:

 

 

      besselk(3:9,[0:.2:9.8 10:.5:20],1) generates the entire 

      71-by-7 table on page 424 of Abramowitz and Stegun,

      "Handbook of Mathematical Functions."

 

 

  See also: BESSELJ1LK10JI, BESSELYZAPJ39, BESSELIZAP039.