ssel Functions with Half O 背景 圆柱体内的 Laplace方程边值问题 10/a 1 a2u a2u ra(T\tr2a02 822 0 au du l=0有界 u=0=f(,2) 分离变量,(0,2)=R()中(0)2(=),就会得
Modified Bessel Functions Bessel Functions with Half Odd Integer Order Spherical Bessel Functions Modified Bessel Equations Modified Bessel Functions Asymptotic Behaviors of Modified Bessel Ftns µ ÎNSLaplace§>¯K 1 r ∂ ∂r r ∂u ∂r + 1 r 2 ∂ 2u ∂φ2 + ∂ 2u ∂z2 = 0 u φ=0 = u φ=2π ∂u ∂φ φ=0 = ∂u ∂φ φ=2π u z=0 = 0 u z=h = 0 u r=0k. u r=a = f(φ, z) ©lCþ§u(r, φ, z) = R(r) Φ(φ)Z(z)§Ò¬ C. S. Wu 1ù μê(n)
ssel Functions with Half O 背景 圆柱体内的 Laplace方程边值问题 10/a 1 a2u a2u ra(T\tr2a02 822 0 au du l=0有界 u=0=f(,2) 分离变量,u(r,φ,z)=B()(刂)z(z),就会得到
Modified Bessel Functions Bessel Functions with Half Odd Integer Order Spherical Bessel Functions Modified Bessel Equations Modified Bessel Functions Asymptotic Behaviors of Modified Bessel Ftns µ ÎNSLaplace§>¯K 1 r ∂ ∂r r ∂u ∂r + 1 r 2 ∂ 2u ∂φ2 + ∂ 2u ∂z2 = 0 u φ=0 = u φ=2π ∂u ∂φ φ=0 = ∂u ∂φ φ=2π u z=0 = 0 u z=h = 0 u r=0k. u r=a = f(φ, z) ©lCþ§u(r, φ, z) = R(r) Φ(φ)Z(z)§Ò¬ C. S. Wu 1ù μê(n)
ssel Functions with Half O 背景 ()+pp()=0 p(0)=p(27)p(0)=(2) z"(z)+AZ(z)=0 z(0)=0 z(h)=0 以及 1 d/ dR R=0 rd d
Modified Bessel Functions Bessel Functions with Half Odd Integer Order Spherical Bessel Functions Modified Bessel Equations Modified Bessel Functions Asymptotic Behaviors of Modified Bessel Ftns µ Φ 00(φ) + µΦ(φ) = 0 Φ(0) = Φ(2π) Φ 0 (0) = Φ 0 (2π) Z 00(z) + λZ(z) = 0 Z(0) = 0 Z(h) = 0 ±9 1 r d dr r dR dr + −λ − µ r 2 R = 0 C. S. Wu 1ù μê(n)
ssel Functions with Half O 背景 本征值 p()+pp(口)=0 cos m (0)=更(2) 本征函数m() p()=(2m) sin no m=0,1,2, AZ(=)=0 (0)=0 本征函数∠n(=)=sn n=1.2.3
Modified Bessel Functions Bessel Functions with Half Odd Integer Order Spherical Bessel Functions Modified Bessel Equations Modified Bessel Functions Asymptotic Behaviors of Modified Bessel Ftns µ Φ 00(φ)+µΦ(φ)=0 Φ(0) = Φ(2π) Φ 0 (0) = Φ 0 (2π) ⇒ µ = m2 ¼ê Φm(φ)=( cos mφ sin mφ m = 0, 1, 2, · · · Z 00(z)+λZ(z)=0 Z(0) = 0 Z(h) = 0 ⇒ λn = nπ h 2 ¼ê Zn(z) = sin nπ h z n = 1, 2, 3, · · · C. S. Wu 1ù μê(n)
ssel Functions with Half O 背景 本征值 p()+pp(口)=0 cos m (0)=更(2) 本征函数m() p()=(2m) sin no m=0,1,2, z"(2)+AZ(x)=0 本征值λ h z(0)=0 本征函数Zn()=sn nt z(h)=0 1,2,3
Modified Bessel Functions Bessel Functions with Half Odd Integer Order Spherical Bessel Functions Modified Bessel Equations Modified Bessel Functions Asymptotic Behaviors of Modified Bessel Ftns µ Φ 00(φ)+µΦ(φ)=0 Φ(0) = Φ(2π) Φ 0 (0) = Φ 0 (2π) ⇒ µ = m2 ¼ê Φm(φ)=( cos mφ sin mφ m = 0, 1, 2, · · · Z 00(z)+λZ(z)=0 Z(0) = 0 Z(h) = 0 ⇒ λn = nπ h 2 ¼ê Zn(z) = sin nπ h z n = 1, 2, 3, · · · C. S. Wu 1ù μê(n)