论文标题
赖特功能相对于参数和其他结果的差异
Differentiation of the Wright functions with respect to parameters and other results
论文作者
论文摘要
在本调查中，我们讨论了赖特功能（第一和第二种）的衍生物。这些功能的差异导致无限功率序列，系数为Digamma（PSI）和伽马功能的商。只有在少数情况下，才有可能以封闭形式获得这些系列的总和。功率序列的功能形式类似于Mittag-Leffler功能的功能序列。如果将赖特函数视为广义贝塞尔函数，则可以根据贝塞尔函数及其衍生物相对于该顺序表示分化操作。可以证明，在许多情况下，可以通过使用Wright功能的Laplace变换执行简单的操作来得出Mittag-Leffler函数的显式形式。针对参数的特定值讨论了两种赖特函数的拉普拉斯变换对。某些变换对通过应用移位的Dirac Delta函数来获得功能限制。
In this survey we discuss derivatives of the Wright functions (of the first and the second kind) with respect to parameters. Differentiation of these functions leads to infinite power series with coefficient being quotients of the digamma (psi) and gamma functions. Only in few cases it is possible to obtain the sums of these series in a closed form. Functional form of the power series resembles those derived for the Mittag-Leffler functions. If the Wright functions are treated as the generalized Bessel functions, differentiation operations can be expressed in terms of the Bessel functions and their derivatives with respect to the order. It is demonstrated that in many cases it is possible to derive the explicit form of the Mittag-Leffler functions by performing simple operations with the Laplace transforms of the Wright functions. The Laplace transform pairs of the both kinds of the Wright functions are discussed for particular values of the parameters. Some transform pairs serve to obtain functional limits by applying the shifted Dirac delta function.
