MATLAB Function Reference Volume 1: A - E - Bad Request

2besselj, bessely
Purpose Bessel functions
Syntax J = besselj(nu,Z) Bessel function of the 1st kind
Y = bessely(nu,Z) Bessel function of the 2nd kind
J = besselj(nu,Z,1)
Y = bessely(nu,Z,1)
[J,ierr] = besselj(nu,Z)
[Y,ierr] = bessely(nu,Z)
Definition The differential equation
z 2
z 2
2
d y
d
z dy
------ z
dz
2 ν 2
+ + ( – )y=
0
besselj, bessely
where ν is a real constant, is called Bessel’s equation, and its solutions are
known as Bessel functions.
Jν( z)
and J– ν(
z)
form a fundamental set of solutions of Bessel’s equation for
noninteger ν . Jν( z)
is defined by
Jν( z)
⎛z -- ⎞
⎝2⎠ ν ∞
= ∑
k = 0
z 2
⎛– ----- ⎞
⎝ 4 ⎠
k
-------------------------------------k!
Γν ( + k + 1)
where Γ( a)
is the gamma function.
Y ν( z)
Jν( z)
Y ν( z)
is a second solution of Bessel’s equation that is linearly independent of
and defined by
Jν( z)
cos( νπ)
– J– ν(
z)
= ----------------------------------------------------------sin(
νπ)
Description J = besselj(nu,Z) computes Bessel functions of the first kind, Jν( z)
, for
each element of the complex array 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
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