Bessel Equation

Bessel equation

[′bes·əl i′kwā·zhən]
(mathematics)
The differential equation z 2ƒ″(z) + z ƒ′(z) + (z 2-n 2)ƒ(z) = 0.

Bessel Equation

 

a linear differential equation of the second order of the form

x2y” + xy’ + (x2 - p2)y = 0

where the parameter (“index”) p can take on arbitrary (complex) values. The equation is named for F. Bessel. Numerous physics problems reduce to this equation. The solutions of the Bessel equation are called cylinder functions.

P. I. LIZORKIN

References in periodicals archive ?
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 [22], 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 [13].
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 [26] and appears as special solutions of inhomogeneous Bessel equations.