Results 241 to 250 of about 11,942,050 (297)

A HIGHER ORDER NON-LINEAR DIFFERENTIAL EQUATION AND A GENERALIZATION OF THE AIRY FUNCTION

Far East Journal of Mathematical Education, 2007
In this paper, a higher order non-linear differential equation is given and it becomes a higher order Airy equation (in our terminology) under the Cole-Hopf transformation. For the even case a solution is explicitly constructed, which is a generalization
K. Fujii
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AN AIRY FUNCTION FOR THE LASER

Journal of Nonlinear Optical Physics & Materials, 1996
We 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, 1985
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Jiachun, Zhao, Dagong
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Algorithm 838

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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Moment integrals of powers of airy functions

ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1993
An 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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On the zeros of generalized Airy functions

ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1991
The authors investigate the log convexity with respect to the parameter \(\gamma\), of the zeros of the generalized Airy functions, which are solutions of the differential equation \((1)\;y''+x^ \gamma y=0,\;x>0\). The results are established using several known facts about the zeros of the Bessel functions.
LAFORGIA, Andrea Ivo Antonio, Elbert, A.
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Appendix A: Airy functions

2000
In this appendix the following are discussed: the Airy differential equation; and zeros of the Airy function.
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Approximation of analytic functions by Airy functions

Integral Transforms and Special Functions, 2008
We 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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Uniform Asymptotic Solution in the Form of an Airy Function for Semiclassical Bound States in One-Dimensional and Radially Symmetric Problems

Theoretical and mathematical physics, 2019
A. Anikin, S. Dobrokhotov, V. Nazaikinskii, A. V. Tsvetkova   +3 more
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Intersection theory on the moduli space of curves and the matrix airy function

, 1992
M. Kontsevich
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