sciences, the Airy function (or Airy function of the first kind) Ai(x) is a special function named after the British astronomer George Biddell Airy (1801–1892)...
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pattern in optics Airy beam, a non-spreading, transversely accelerating optical wavepacket Airy function, a mathematical function Airy points, support points...
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the Airy zeta function, studied by Crandall (1996), is a function analogous to the Riemann zeta function and related to the zeros of the Airy function. The...
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Stokes phenomenon (section Example: the Airy function)
cut) because these approximations contain multi-valued functions. In contrast, the Airy function is single valued and indeed entire and therefore, in order...
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Sir George Biddell Airy KCB FRS (/ˈɛəri/; 27 July 1801 – 2 January 1892) was an English mathematician and astronomer, as well as the Lucasian Professor...
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modular forms, which include J-invariant Dedekind eta function Airy function Bessel functions: Defined by a differential equation; useful in astronomy...
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the Euler–Tricomi equation of transonic gas dynamics, is the rescaled Airy function ε − 1 / 3 Ai ( x ε − 1 / 3 ) . {\displaystyle \varepsilon ^{-1/3}\operatorname...
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} Zeta functions include: Airy zeta function, related to the zeros of the Airy function Arakawa–Kaneko zeta function Arithmetic zeta function Artin–Mazur...
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In optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best-focused spot of light that a perfect lens with a circular aperture...
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product of two sinc functions vs. an Airy function, respectively. Conventions: w 0 ( x ) {\displaystyle w_{0}(x)} is a zero-phase function (symmetrical about...
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and so the edge of the rainbow always has the shape of an Airy function. The same Airy function fold catastrophe can be seen in nuclear-nuclear scattering...
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Witten conjecture (redirect from Matrix Airy function)
"Intersection theory on the moduli space of curves and the matrix Airy function", Communications in Mathematical Physics, 147 (1): 1–23, Bibcode:1992CMaPh...
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produces an Airy disc in the image plane. The argument of the function J1(x)/x is important, because this determines the scaling of the Airy disc (in other...
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equations are entire functions. For example, the exponential function, sine, cosine, Airy functions and Parabolic cylinder functions arise in this way....
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almost everywhere. AFSOC - Assume for the sake of contradiction Ai – Airy function. AL – Action limit. Alt – alternating group (Alt(n) is also written...
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an Airy equation. In the new coordinates the equation is solved by the Airy function. Georgios Sivilioglou, et al. successfully fabricated an Airy beam...
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"point spread function" viewpoint would be to ask how well a lens transforms an Airy function in the object plane into an Airy function in the image plane...
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{\frac {1}{4n{\sqrt {3}}}}e^{\pi {\sqrt {\frac {2n}{3}}}}} Airy function The Airy function, Ai(x), is a solution of the differential equation y″ − xy...
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Fabry–Pérot interferometer (section Generic Airy distribution: The internal resonance enhancement factor)
resolved. Therefore, the Airy distribution becomes the underlying fundamental function and the measurement delivers a sum of Airy distributions. The parameters...
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Wave packet (section The Airy wave train)
group velocity, and always disperses, there exists a wave function based on Airy functions, that propagates freely without envelope dispersion, maintaining...
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process with almost surely continuous sample paths. The Airy process is named after the Airy function. The process can be defined through its finite-dimensional...
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Abel: Abel polynomials - Abelian function - Abel–Gontscharoff interpolating polynomial Sir George Biddell Airy: Airy function Waleed Al-Salam (1926–1996):...
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classical explanation, but can be modeled using an Airy function. Using properties of the Airy function, one may estimate the probability of finding the...
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differential equation is known as the Airy equation, and the solution may be written in terms of Airy functions, Ψ ( x ) = C A Ai ( U 1 3 ⋅ ( x − x...
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Ringing artifacts (section Special functions)
Fraunhofer diffraction yields the Airy disk as point spread function, which has a ringing pattern. The Bessel function of the first kind, J 0 , {\displaystyle...
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conditions. The Airy stress function is a special case of the Maxwell stress functions, in which it is assumed that A=B=0 and C is a function of x and y only...
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solution to connect them. Hence, the Airy function solutions will asymptote into sine, cosine and exponential functions in the proper limits. The relationships...
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Hermite polynomials (redirect from Hermite function)
{1}{6}}t\right)+O\left(n^{-{\frac {2}{3}}}\right)\right),} where Ai is the Airy function of the first kind. The physicist's Hermite polynomials evaluated at...
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transmission, or a mechanical structure. In optics, it is primarily used to remove Airy disks caused by diffraction around an intensity peak, improving the focus...
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neural networks. In fluorescence microscopy a 2D Gaussian function is used to approximate the Airy disk, describing the intensity distribution produced by...
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