Bessel functions are mathematical special functions that commonly appear in problems involving wave motion, heat conduction, and other physical phenomena...

expresses any given function f(r) as the weighted sum of an infinite number of Bessel functions of the first kind Jν(kr). The Bessel functions in the sum are...

mathematical analysis, the Bessel–Clifford function, named after Friedrich Bessel and William Kingdon Clifford, is an entire function of two complex variables...

important mathematical functions were first studied systematically by Bessel and were named Bessel functions in his honour. Bessel was born in Minden, Westphalia...

known as the Kaiser–Bessel window, was developed by James Kaiser at Bell Laboratories. It is a one-parameter family of window functions used in finite impulse...

Kaiser window which is defined in terms of a modified Bessel function. This hybrid window function was introduced to decrease the peak side-lobe level of...

Fourier–Bessel series is a particular kind of generalized Fourier series (an infinite series expansion on a finite interval) based on Bessel functions. Fourier–Bessel...

In mathematics, a Jackson q-Bessel function (or basic Bessel function) is one of the three q-analogs of the Bessel function introduced by Jackson (1906a...

In mathematics, the Bessel–Maitland function, or Wright generalized Bessel function, is a generalization of the Bessel function, introduced by Edward...

Γ {\displaystyle \Gamma } is the gamma function, K ν {\displaystyle K_{\nu }} is the modified Bessel function of the second kind, and ρ and ν {\displaystyle...

reverse Bessel polynomial is used in the design of Bessel electronic filters. The Bessel polynomial may also be defined using Bessel functions from which...

A Bessel beam is a wave whose amplitude is described by a Bessel function of the first kind. Electromagnetic, acoustic, gravitational, and matter waves...

(Rayleigh's formula) for the zeroth-order spherical Bessel function of the first kind. The sinc function has two forms, normalized and unnormalized. In mathematics...

called Bessel–Thomson filters in recognition of W. E. Thomson, who worked out how to apply Bessel functions to filter design in 1949. The Bessel filter...

Heaviside step function, J ν ( z ) {\textstyle J_{\nu }(z)} is a Bessel function, I ν ( z ) {\textstyle I_{\nu }(z)} is a modified Bessel function of the first...

carrier modulated by such a sinusoidal signal can be represented with Bessel functions; this provides the basis for a mathematical understanding of frequency...

in turn have many particular special functions as special cases, such as elementary functions, Bessel functions, and the classical orthogonal polynomials...

The variance-gamma distribution, generalized Laplace distribution or Bessel function distribution is a continuous probability distribution that is defined...

Bessel may refer to: Bessel beam Bessel ellipsoid Bessel function in mathematics Bessel's inequality in mathematics Bessel's correction in statistics Bessel...

Second synchrotron function G ( x ) = x K 2 3 ( x ) {\displaystyle G(x)=xK_{\frac {2}{3}}(x)} where Kj is the modified Bessel function of the second kind...

Dedekind eta function Airy function Bessel functions: Defined by a differential equation; useful in astronomy, electromagnetism, and mechanics. Bessel–Clifford...

incomplete Bessel functions are types of special functions which act as a type of extension from the complete-type of Bessel functions. The incomplete Bessel functions...

mathematics, the Hahn–Exton q-Bessel function or the third Jackson q-Bessel function is a q-analog of the Bessel function, and satisfies the Hahn-Exton...

identity represents the Lorentz factor in terms of an infinite series of Bessel functions: ∑ m = 1 ∞ ( J m − 1 2 ( m β ) + J m + 1 2 ( m β ) ) = 1 1 − β 2 ....

uniform function over a circular area (in one FT domain) corresponds to J1(x)/x in the other FT domain, where J1(x) is the first-order Bessel function of the...

{1}{\varepsilon }}}^{\frac {1}{\varepsilon }}\cos(kx)\,dk} and the Bessel function η ε ( x ) = 1 ε J 1 ε ( x + 1 ε ) . {\displaystyle \eta _{\varepsilon...

the Bessel function J α ( x ) {\displaystyle J_{\alpha }(x)} . a m {\displaystyle a_{m}} is the m {\displaystyle m} -th zero of the Airy function Ai ⁡...

density function f Z ( z ) = π − 1 K 0 ( | z | ) {\textstyle f_{Z}(z)=\pi ^{-1}K_{0}(|z|)} where K 0 {\textstyle K_{0}} is the modified Bessel function of...

the Bessel function of the first kind with order ⁠n + 2k − 2/2⁠. When k = 0 this gives a useful formula for the Fourier transform of a radial function. This...

\operatorname {arctg} } , or tan − 1 {\displaystyle \tan ^{-1}} . The Bessel functions may be denoted J n ( x ) , {\displaystyle J_{n}(x),} besselj ⁡ ( n...