Asymptotic and structural properties of special cases of the Wright function arising in probability theory

作者：Paris Richard B^*; Vinogradov Vladimir

来源：Lithuanian Mathematical Journal, 2016, 56(3): 377-409.

DOI：10.1007/s10986-016-9324-1

• Wright function
• asymptotics
• exponentially small expansions
• algebraic expansions
• Stokes lines
• reflection principle
• multiplication property
• Airy function
• Bessel functions
• confluent hypergeometric function
• Whittaker function

This paper presents previously unknown properties of some special cases of the Wright function whose consideration is necessitated by our work on probability theory. We establish new asymptotic properties of this function under numerous assumptions on the ordering of the parameter and variable. Several representations involving well-known special functions are given. We also provide some integral representations and structural properties involving the "reduced" Wright function. Some of the properties established imply a reflection principle that connects the "reduced" Wright functions with the opposite values of the parameter and certain Bessel functions. Several asymptotic relations for both particular cases of this function are also given.

• 出版日期2016-7