Bessel functions, named after Friedrich Bessel who was the first to systematically study them in 1824, are canonical solutions y(x) of Bessel's differential...

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...

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...

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...

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...

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

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

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...

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

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...

his expression (Rayleigh's formula) for the zeroth-order spherical Bessel function of the first kind. The zero crossings of the unnormalized sinc are...

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

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...

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...

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...

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 ....

{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...

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

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

contains functions for calculating sine, cosine, arctangent, natural logarithm, the exponential function and the two parameter Bessel function J. Most...

t)=e^{-t}I_{n}(t)} where I n ( t ) {\displaystyle I_{n}(t)} denotes the modified Bessel functions of integer order. This is the discrete analog of the continuous Gaussian...

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

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...

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

z)=(1+z)e^{z}.} Bateman's function Bessel functions and many related functions such as Airy functions, Kelvin functions, Hankel functions. For example, in the...

modified Bessel functions) For negative arguments, the Airy function are related to the Bessel functions: Ai ⁡ ( − x ) = x 9 [ J 1 / 3 ( 2 3 x 3 / 2 ) + J − 1...