Equation (5) is zero-order Bessel equation
with imaginary argument, and its Laplace spatial solution is
29) is a classic form of the zero-order Bessel equation
whose solution is:
Another approach to solving (26), one that does not require that it be recognized as a Bessel equation, is to use an iterative numerical method.
Directly or indirectly all three of these quantities result from solving the Bessel equation (26), which, itself, is derived from the substitute equation (13), not from the fundamental, definition of a force-free current (12).
Tangential component of the AM magnetic field is described by inhomogeneous Bessel equation
, which right-hand part [F.
ik] mentioned above, one can find a Bessel-type equation for the magnetic component of the wave field similar to the modified Bessel equation
for the wave field in the plasma .
2]] refers to Bessel equation
, the singularity type [2/x]-[[l(l + 1)]/[x.
the Bessel equation
is LCO, LCN, or LP in different ranges of parameter v--it is easier to ask a user to input such parameter ranges manually and check them, rather than write an algorithm to determine the ranges automatically.
One of these yields the factor [Mathematical Expression Omitted], and the other is a Bessel equation
By using the separation of variables, the magnetic field equations in regions II, III and IV governed by the Laplace's equation can be decomposed into a Helmholtz equation and a Bessel equation
The general Fourier-Bessel Integral on [a,[infinity]), a [is greater than] 0, associated with the Bessel equation
of order 0 in Liouville Normal Form,
1] is the modified Struve functions  and appears as special solutions of inhomogeneous Bessel equations