Bessel functions of the first kind.
J = BESSELJ(ALPHA,X) computes Bessel functions of the first kind,
J _sub_alpha(X) for real, non-negative order ALPHA and argument X.
In general, both ALPHA and X may be vectors. The output J is
an m-by-n matrix with m = lenth(X), n = length(ALPHA) and
J (i,k) = J _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.
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.
J _sub_2/3(r) matches the singularity at the interior corner
where the angle is pi/(2/3).
See also: BESSELY , BESSELI , BESSELK .