The theory of Generalized Bessel Functions is reviewed and their application to various problems in the study of electro-magnetic processes is presented. We consider the cases of emission of bremsstrahlung radiation by ultra-relativistic electrons in linearly polarized undulators, including also exotic configurations, aimed at enhancing the harmonic content of the emitted radiation. The analysis is eventually extended to the generalization of the FEL pendulum equation to treat Free Electron Laser operating with multi-harmonic undulators. The paper aims at picking out those elements supporting the usefulness of the Generalized Bessel Functions in the elaboration of the theory underlying the study of the spectral properties of the bremsstrahlung radiation emitted by relativistic charges, along with the relevant flexibility in accounting for a large variety of apparently uncorrelated phenomenolgies, like multi-photon processes, including non linear Compton scattering.

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广义贝塞尔函数及其在Bre致发光和多光子过程中的应用

综述了广义贝塞尔函数的理论，并提出了它们在电磁过程研究中的各种应用。我们考虑了在线性极化波荡器中由超相对论电子发射致辐射的情况，其中还包括奇异结构，旨在增强发射辐射的谐波含量。该分析最终扩展到FEL摆方程的一般化，以处理使用多谐波波荡器工作的自由电子激光器。本文旨在挑选出支持广义贝塞尔函数有用性的那些元素，以阐述有关相对论电荷发射的致辐射的光谱特性的理论基础，