抛物柱面函数的Nield-Kuznetsov函数和拉普拉斯变换
Nield-Kuznetsov functions and Laplace transforms of parabolic cylinder functions
摘要：
研究了第一类Nield-Kuznetsov函数，它是非齐次抛物型Weber方程的解，并在流体流动问题中有应用。构造了它们之间的连接公式、齐次型微分方程的数值满意解和一个新的互补Nield-Kuznetsov函数。渐近展开，然后推导出一致有效的大值的参数和无界的实值和复值的参数。拉普拉斯变换的抛物柱面函数$W(a,x)$和$U(a,x)$随后被证明是明确表示的补充Nield-Kuznetsov功能和密切相关的功能，并从这些统一的渐近展开的积分。
英文摘要：
Nield-Kuznetsov functions of the first kind are studied, which are solutions of an inhomogeneous parabolic Weber equation, and have applications in fluid flow problems. Connection formulas are constructed between them, numerically satisfactory solutions of the homogeneous version of the differential equation, and a new complementary Nield-Kuznetsov function. Asymptotic expansions are then derived that are uniformly valid for large values of the parameter and unbounded real and complex values of the argument. Laplace transforms of the parabolic cylinder functions $W(a,x)$ and $U(a,x)$ are subsequently shown to be explicitly represented in terms of the complementary Nield-Kuznetsov function and closely related functions, and from these uniform asymptotic expansions are derived for the integrals.
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