In this review paper, we stress the importance of the higher transcendental Wright functions of the second kind in the framework of Mathematical Physics. We first start with the analytical properties of the classical Wright functions of which we distinguish two kinds. We then justify the relevance of the Wright functions of the second kind as fundamental solutions of the time-fractional diffusion-wave equations. Indeed, we think that this approach is the most accessible point of view for describing non-Gaussian stochastic processes and the transition from sub-diffusion processes to wave propagation. Through the sections of the text and suitable appendices, we plan to address the reader in this pathway towards the applications of the Wright functions of the second kind.

中文翻译：

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数学中的第二种赖特函数

在这篇综述论文中，我们强调了在数学物理学框架中第二种高级先验赖特函数的重要性。我们首先从经典的Wright函数的解析性质入手，我们将其分为两种。然后，我们证明第二种Wright函数作为时间分数阶扩散波方程的基本解的相关性。确实，我们认为这种方法是描述非高斯随机过程以及从子扩散过程到波传播的过渡的最容易理解的观点。通过本书的各节和适当的附录，我们计划以这种途径向读者介绍第二种Wright功能的应用。