Autoconvolution equations and special functions
Autoconvolution equations and special functions
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DOI：
10.1080/10652460701754786
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发表时间：
2008-10
影响因子：
1
通讯作者：
L. von Wolfersdorf
中科院分区：
文献类型：
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作者：
L. von Wolfersdorf
对广义Mittag-Leffler函数E α，β，误差函数和广义沃尔泰拉函数ν，μ等几类特殊函数，导出了第三类自卷积方程.这些方程推广了伯恩斯坦和Doetsch关于Mittag-Leffler函数E α的著名方程和Janno和作者关于沃尔泰拉函数ν的方程。此外，还给出了误差函数的第一类自卷积方程和沃尔泰拉函数导数的两个具有自卷积积分的积分微分方程.
Autoconvolution equations of the third kind are derived for some classes of special functions as generalized Mittag–Leffler functions E α, β, error functions, and generalized Volterra functions ν, μ. These equations generalize the well-known equation by Bernstein and Doetsch for the Mittag–Leffler function E α and an equation by Janno and the author for the Volterra function ν. In addition, some autoconvolution equations of the first kind for error functions and two integro-differential equations with autoconvolution integral for the derivative of Volterra functions are given.