Definite integral of the product of hermite functions, with applications to the theory of nonlinear interactions among equatorial waves
Definite integral of the product of hermite functions, with applications to the theory of nonlinear interactions among equatorial waves
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Hermite函数乘积的定积分及其在赤道波非线性相互作用理论中的应用
DOI：
10.1029/jc088ic14p09741
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发表时间：
1983
影响因子：
--
通讯作者：
P. Ripa
中科院分区：
文献类型：
--
作者：
P. Ripa
给出了Hermite函数乘积的定积分的解析表达式和渐近估计，Hermite多项式乘以Gaussian）。每个Hermite函数的幅角与积分变量成比例但不一定相等。渐近估计被用来表明，积分是可以忽略不计的，除非有当地波数的总和为零的点。在地球物理流体动力学的背景下，这一结果被用来建立赤道波（由Hermite函数表示）和中纬度波（由正弦曲线表示）的纬向相互作用条件之间的联系：对于后者，必须为零的常数波数之和
An analytic expression and an asymptotic estimate are derived for the definite integral of a product of Hermite functions (i.e., a Hermite polynomial times a Gaussian). The argument of each Hermite function is proportional but not neccesarily equal to the integration variable. The asymptotic estimate is used to show that the integral is negligible unless there are points where the sum of the local wave numbers is zero. This result is used, in the context of geophysical fluid dynamics, to establish a connection between the meridional interaction condition for equatorial waves, represented by Hermite functions, and midlatitude waves, represented by sinusoids: for the latter it is the sum of the constant wavenumbers that has to vanish