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標題: 圓柱方程式
On The Cylinder Equations
作者: 劉瓊文
Chiung-Wen Liu
關鍵字: 圓柱
cylinder equations
Bessel equations
引用: [1] M. Abramowitz and I. A. Stegun (Eds.).r, Bessel Functions (chapter9 in Handbook of Mathe- matical Functions with Formulas, Graphs, and Mathematical Tables), 9th printing, New York: Dover, pp. 358-364, 1972. [2] Richard Beals and Roderick Wong, Special Functions: A Graduate Text (Cambridge Studies in Advanced Mathematics),Publisher Cambridge University Press, 2010. [3] Paul Blanchard, Robert L. Devaney, Glen R. Hall, Differential Equations,Brooks/Cole Pub- lishing Co., 2002. [4] Boyce and Richard C. DiPrima, Elementary Differential Equations 9th Edition,Wiley, 2008. [5] Mark W. Coffey, ,Integral and series representations of the digammaand polygamma func- tions,Department of PhysicsColorado School of MinesGolden, CO 80401(Received 2010)August 10, 2010. [6] D. Gilbarg and N. S. Trudinger,Elliptic partial differential equations of second order, 2nd edi- tion, Springer Verlag, 1983. [7] Jeffrey C. Lagarias,Euler’s constant: Euler’s Work and Modern Developments,Bulletin of Amer- ican Mathematical Society, 2013. [8] Pascal Sebah and Xavier Gourdon,Introduction to the Gamma Function,American Journal of Scientific Reasearch,2002.
摘要: 令 u(x) = ϕ(|x|) 滿足 ∆ρu(x) := Du(x)−ρu(x)=0, ρ>0 , 則 ϕ(r) 滿足Bessel方程式 (0.1) ϕ''(r)+ϕ''(r)/r−ρϕ(r)=0, if x ∈ R^2 or (0.2) ϕ''(r)+(n−1/r)ϕ''(r)−ρϕ(r)=0, if x ∈ R^n ,for n≥ 3. 在本論文中''我們計劃去找微分方程 (0.1) 和 (0.2) 的解。
Let u(x) = ϕ(|x|) satisfy ∆ρu(x) := Du(x) − ρu(x) = 0, where ρ > 0. Then ϕ(r) satisfies the Bessel equation (0.1) ϕ''(r)+ϕ''(r)/r−ρϕ(r)=0, if x ∈ R^2 or (0.2) ϕ''(r)+(n−1/r)ϕ''(r)−ρϕ(r)=0, if x ∈ R^n ,for n≥ 3. In this thesis, we intend to solve the solutions of (0.1) and (0.2) with n = 3.
文章公開時間: 2018-08-24
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