Question

matlab 中的贝塞尔函数：Y= BesselJ(0,2) 这个是什么意思？

它是指求变量x=2时的0阶贝塞尔函数吗?

Answer 1

Y= BesselJ(0,2)
是指变量为2时的，0阶的第一类贝塞尔函数！

贝塞尔函数的一族，也称第一类贝塞尔函数，记作Jn（x），用x的偶次幂的无穷和来定义，数 n称为贝塞尔函数的阶，它依赖于函数所要解决的问题。J0 （x）的图形像衰减的余弦曲线，J1（x）像衰减的正弦曲线。

Answer 2

贝塞尔函数分为几类，看看以下帮助，也许有所启发。

>> help Bessel
BESSEL Bessel functions of various kinds.
Bessel functions are solutions to Bessel's differential
equation of order NU:
2 2 2
x * y'' + x * y' + (x - nu ) * y = 0

There are several functions available to produce solutions to
Bessel's equations. These are:

BESSELJ(NU,Z) Bessel function of the first kind
BESSELY(NU,Z) Bessel function of the second kind
BESSELI(NU,Z) Modified Bessel function of the first kind
BESSELK(NU,Z) Modified Bessel function of the second kind
BESSELH(NU,K,Z) Hankel function
AIRY(K,Z) Airy function

See the help for each function for more details.

>> help BesselJ
BESSELJ Bessel function of the first kind.
J = BESSELJ(NU,Z) is the Bessel function of the first kind, J_nu(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.

J = BESSELJ(NU,Z,0) is the same as BESSELJ(NU,Z).

J = BESSELJ(NU,Z,1) scales J_nu(z) by exp(-abs(imag(z)))

[J,IERR] = BESSELJ(NU,Z) also returns an array of error flags.
ierr = 1 Illegal arguments.
ierr = 2 Overflow. Return Inf.
ierr = 3 Some loss of accuracy in argument reduction.
ierr = 4 Complete loss of accuracy, z or nu too large.
ierr = 5 No convergence. Return NaN.

Examples:

besselj(3:9,(0:.2:10)') generates the entire table on page 398
of Abramowitz and Stegun, Handbook of Mathematical Functions.

MEMBRANE uses BESSELJ to generate the fractional order Bessel
functions used by the MathWorks Logo, the L-shaped membrane.

This M-file uses a MEX interface to a Fortran library by D. E. Amos.

Class support for inputs NU and Z:
float: double, single

See also bessely, besseli, besselk, besselh.

Answer 3

yes