Bessel function


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Bessel function

[′bes·əl ‚fəŋk·shən]
(mathematics)
A solution of the Bessel equation. Also known as cylindrical function. Symbolized Jn (z).
References in periodicals archive ?
where [J.sub.[mu]] the Bessel function of the first kind of order [mu] and {[j.sub.[mu],n}.sup.[infinity].sub.n=1] 1 is the increasing sequence of positive zeros of [J.sub.[mu]] (cf.
Key words: Voigt function; Bessel function; Parabolic function; Hypergeometric function andLaguerre polynomials.
Where [J.sub.0] is the Bessel function of complex order argument 0, i = [square root of (-1)] is the imaginary unit, r is the radial coordinate and Re means that the real part of the resulting complex number is taken.
One mathematical description of these structures is called the "Bessel Function Model".
(iv) Several implementation details for algorithm optimization including Woodbury matrix identity for dimension-reduction, pruning a basis function and the third kind Bessel function approximation are discussed, and the CRB of DOA estimation is derived.
A solution of the generalized Bessel differential equation is the generalized Bessel function of order v and degree [mu] specified by the power series with infinite radius of convergence
If c = 1 and k [right arrow] 1, then the generalized k-Bessel function defined in (1) reduces to the classical Bessel function [J.sub.v] defined in Erdelyi [3].
where R(p) > 0; [K.sub.v](x) is the Bessel function of the second kind defined by ([18], p.
[I.sub.0]([[beta].sub.m]r) is the zero-order modified Bessel function. The partial differentials of the function y to r and z are the two velocity solutions, [u.sub.r] and [u.sub.z], which are shown below:
Using the integral form of the Bessel function and the limitation N [right arrow] [infinity], the normalized radiation vector [??]([theta], [phi], z) of the array can be deduced as:
(Here [J.sub.v] is Bessel function of the first kind of order v [13].) Let
where [J.sub.[alpha]] denotes the usual Bessel function of first kind and order [alpha].