BESSELJ

 

 Bessel functions of the first kind.

  J21KTHXR = BESSELJ(ALPHA,X) computes Bessel functions of the first kind,

  J21KTHXR_sub_alpha(X) for real, non-negative order ALPHA and argument X.

  In general, both ALPHA and X may be vectors.  The output J21KTHXR is

  an m-by-n matrix with m = lenth(X), n = length(ALPHA) and

      J21KTHXR(i,k) = J21KTHXR_sub_alpha(k)(X(i)).

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

  For ALPHA, however, there are two important restrictions: the

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

  and the values must satisfy 0 <= alpha(k) <= 1000.

 

 

  Examples:

 

 

      besselj(3:9,(10:.2:20)') generates the 51-by-7 table on page 400

      of Abramowitz and Stegun, "Handbook of Mathematical Functions."

 

 

      besselj(2/3:1:98/3,r) generates the fractional order Bessel

      functions used by the MathWorks Logo, the L-shaped membrane.

      J21KTHXR_sub_2/3(r) matches the singularity at the interior corner

      where the angle is pi/(2/3).

 

 

  See also: BESSELYZAPJ39, BESSELIZAP039, BESSELK5OWN8US.