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laguerre函数
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  laguerre function
    In consideration of the factor that the energy of the induced current on a scattering object excited by a plane wave with a Gaussian pulse almost all concentrates on a finite time and frequency-domain, by expanding the response in time with Laguerre function, a corresponding frequency-domain response is attained by using Fourier transform.
    考虑到散射体在高斯脉冲平面波激励下感应电流的能量几乎全部集中在有限时间和频率的范围内这一因素,将时域响应用Laguerre函数展开,并由傅里叶变换,可得到相应的频域响应。
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  laguerre function
The Laguerre function and the radial Coulomb wave function are defined by their recursion relations.
      
An addition theorem for the Laguerre function is re-derived using these techniques.
      
The characteristics of the principal modes and the multi-input threshold device can be derived from Laguerre function expansions of the computed first- and second-order Volterra kernels when the system is stimulated with a randomly varying input.
      
The new function is a generalization of the q-Laguerre function and the Stieltjes-Wigert function.
      
Finally, limq→1Anα((1 - q)x, -β, 1;q) gives Ln(α,β)(x,q), which is a β-modification of the ordinary Laguerre function.
      
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In consideration of the factor that the energy of the induced current on a scattering object excited by a plane wave with a Gaussian pulse almost all concentrates on a finite time and frequency-domain, by expanding the response in time with Laguerre function, a corresponding frequency-domain response is attained by using Fourier transform. According to the characters of Fourier transform, the low-frequency and high-frequency responses determine the late-time and early-time responses respectively. In this paper,...

In consideration of the factor that the energy of the induced current on a scattering object excited by a plane wave with a Gaussian pulse almost all concentrates on a finite time and frequency-domain, by expanding the response in time with Laguerre function, a corresponding frequency-domain response is attained by using Fourier transform. According to the characters of Fourier transform, the low-frequency and high-frequency responses determine the late-time and early-time responses respectively. In this paper, the early-time and low-frequency responses are generated through the use of a time-and-frequency hybrid method including MOT and MOM and they are mutually complementary and contain all the necessary information. So the whole response can be attained by simultaneous extrapolation in time and frequency domains. The electromagnetic scattering responses in the time and frequency domains of the ideal metal conductors are calculated and analyzed by using this method.

考虑到散射体在高斯脉冲平面波激励下感应电流的能量几乎全部集中在有限时间和频率的范围内这一因素,将时域响应用Laguerre函数展开,并由傅里叶变换,可得到相应的频域响应。采用时间步进法(MOT)和矩量法(MOM)分别得到早时和低频响应,由早时响应和低频响应信息的互补关系,联合外推得到整个时、频响应。用本方法分析计算了理想金属导线的时、频域电磁散射响应,结果表明了该方法与频域MOM、时域MOT的精确数值解非常接近。

 
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