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)...

pattern in optics Airy beam, a non-spreading, transversely accelerating optical wavepacket Airy function, a mathematical function Airy points, support points...

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...

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...

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...

cut) because these approximations contain multi-valued functions. In contrast, the Airy function is single valued and indeed entire and therefore, in order...

modular forms, which include J-invariant Dedekind eta function Airy function Bessel functions: Defined by a differential equation; useful in astronomy...

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...

} Zeta functions include: Airy zeta function, related to the zeros of the Airy function Arakawa–Kaneko zeta function Arithmetic zeta function Artin–Mazur...

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...

equations are entire functions. For example, the exponential function, sine, cosine, Airy functions and Parabolic cylinder functions arise in this way....

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...

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...

group velocity, and always disperses, there exists a wave function based on Airy functions, that propagates freely without envelope dispersion, maintaining...

"Intersection theory on the moduli space of curves and the matrix Airy function", Communications in Mathematical Physics, 147 (1): 1–23, Bibcode:1992CMaPh...

almost everywhere. AFSOC - Assume for the sake of contradiction Ai – Airy function. AL – Action limit. Alt – alternating group (Alt(n) is also written...

an Airy equation. In the new coordinates the equation is solved by the Airy function. Georgios Sivilioglou, et al. successfully fabricated an Airy beam...

"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...

{\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...

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...

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...

\left(-{\frac {t^{3}}{3}}+xt\right)\,dt.} The Scorer's functions can also be defined in terms of Airy functions: G i ( x ) = B i ( x ) ∫ x ∞ A i ( t ) d t + A...

classical explanation, but can be modeled using an Airy function. Using properties of the Airy function, one may estimate the probability of finding the...

problem, many-body problem Ballistics Airy function Bessel function Legendre polynomials Hypergeometric function Angular velocity Angular momentum Angular...

resolved. Therefore, the Airy distribution becomes the underlying fundamental function and the measurement delivers a sum of Airy distributions. The parameters...

H_{k}(x)} is the k {\displaystyle k} th Hermite polynomial. The Airy process has kernel function K A i ( x , y ) = Ai ⁡ ( x ) Ai ′ ⁡ ( y ) − Ai ⁡ ( y ) Ai ′...

solution to connect them. Hence, the Airy function solutions will asymptote into sine, cosine and exponential functions in the proper limits. The relationships...

{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...

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...

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...