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AN AIRY FUNCTION FOR THE LASER
Journal of Nonlinear Optical Physics & Materials, 1996We give a general equation which allows the description of the evolution of the laser properties when the gain is varied from below to above threshold. The method is general in the context of the semi-classical theory of lasers. It is numerically illustrated in the simplest case of a single mode laser with a source term characterized by a very narrow ...
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Generalized airy functions with complex variables
Applied Mathematics and Mechanics, 1985zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Jiachun, Zhao, Dagong
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2000
In this appendix the following are discussed: the Airy differential equation; and zeros of the Airy function.
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In this appendix the following are discussed: the Airy differential equation; and zeros of the Airy function.
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ACM Transactions on Mathematical Software, 2004
We present a Fortran 90 module, which computes the solutions and their derivatives of Airy's differential equation, both on the real line and in the complex plane. The module also computes the zeros and associated values of the solutions and their derivatives, and the modulus and phase functions on the negative real axis.
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We present a Fortran 90 module, which computes the solutions and their derivatives of Airy's differential equation, both on the real line and in the complex plane. The module also computes the zeros and associated values of the solutions and their derivatives, and the modulus and phase functions on the negative real axis.
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On the Reversion of an Asymptotic Expansion and the Zeros of the Airy Functions
SIAM Review, 1999Summary: The general theories of the derivation of inverses of functions from their power series and asymptotic expansions are discussed and compared. The asymptotic theory is applied to obtain asymptotic expansions of the zeros of the Airy functions and their derivatives, and also of the associated values of the functions or derivatives.
Bruce R. Fabijonas, Frank W. J. Olver
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Moment integrals of powers of airy functions
ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1993An analytic approach to compute integrals: \(J_ n(\alpha)=\int^ \infty_ 0z^ n\bigl[Ai(z)\bigr]^ \alpha dz\), \(J_ n'(\alpha)=\int_ 0^ \infty\bigl[Ai'(z)\bigr]^ \alpha dz\) is presented, where \(Ai'[z]\) is the derivative of the Airy function \(Ai(z)\) and \(\alpha\) is any real number.
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Approximation of analytic functions by Airy functions
Integral Transforms and Special Functions, 2008We solve the inhomogeneous Airy differential equation and apply this result to prove that every analytic function can be approximated, on a restricted domain, by an appropriate ‘Airy function’ with an error bound described by a quadratic function.
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Integrals of products of Airy functions
Journal of Physics A: Mathematical and General, 1977A large number of indefinite integrals of the form integral xny1y2dx have been evaluated in terms of x, y1, y2 and their first derivatives; y1 and y2 are both solutions of the differential equation y=xy. Some of these integrals can be applied to the quantum mechanical problem of a particle in a uniform field of force.
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