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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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...
94 KB (14,004 words) - 01:51, 12 September 2024
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...
43 KB (5,033 words) - 13:52, 12 August 2024
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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} 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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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...
73 KB (8,651 words) - 20:46, 29 July 2024
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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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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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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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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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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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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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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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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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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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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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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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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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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Strehl ratio (section The Airy disk)
point spread function (PSF) which describes the image formed from an object with no spatial extent (a "point source"), is given by the Airy disk as illustrated...
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