B = bessel(alpha,x)
is called Bessel's equation, and its solutions are known as Bessel functions.
B = bessel(alpha x) computes Bessel functions of the first kind, or modified Bessel functions of the first kind, for real, nonnegative
alpha and nonnegative
x(no imaginary component),
besseljfunction to compute the Bessel function of the first kind.
x(no real component),
besselifunction to compute the modified Bessel function of the first kind.
x(both real and imaginary component),
besselafunction to compute the Bessel function of the first kind.
alphais a scalar and
xis a vector,
Bis a vector the same length as
xis a vector of length
alphais a vector of length
bessel(alpha(k), x(i)). The elements of
xcan be any nonnegative values, in any order. For
alpha, the increment between elements must be 1, and all elements must be between 0 and 1000, inclusive.
x = 0:.25:10;
besselcalls the function
besseljevaluates the Bessel function using three-term recurrence for small-valued
x, or an asymptotic series for large
x. For purely complex
besseli, which uses three-term backward recurrence for most
x, and an asymptotic expansion for large
x. For complex
bessela, which uses either a power series or an asymptotic expansion depending on roundoff error considerations. See reference .
For some values of arguments,
bessela's results may be severely contaminated by roundoff error.
[J,digits] = bessela(alpha,x) returns an estimate of the number of correct significant digits in the computed result.
digits is the
log10 of the estimated relative error, so a value of 14 or 15 corresponds to nearly full accuracy in IEEE or VAX arithmetic, while 1 or 2 indicates nearly useless results. Any negative value of digits is replaced by zero, the corresponding
J set to
NaN and a division by zero warning message is generated. If either
x is less than 50, digits are at least 8. In the
(alpha,x) plane, the region of least accuracy is near the line
alpha = x, so small values of
alpha and large values of
x, or vice versa, give the most accurate results. For example:
---------------- x alpha digits ----------------
(c) Copyright 1994 by The MathWorks, Inc.