Bessel Functions with 1 d dw d d 2)()=0的解是 (2)=CJm(2)+DNm(2) 1 d/d d d y(x)=0的解是 y()=CJm(iz)+ DNm(iaz 1 d/ dh B=0的解是
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 1 z d dz z dw dz + 1 − m2 z 2 w(z) = 0)´ w(z) = CJm(z) + DNm(z) 1 x d dx x dy dx + −1 − m2 x 2 y(x) = 0)´ y(x) = CJm(ix) + DNm(ix) 1 r d dr r dR dr + − nπ h 2 − m2 r 2 R = 0)´ R(r) = CJm inπ h r + DNm inπ h r C. S. Wu 1ù μê(n)
Bessel Functions with 1 d dw d d 2)()=0的解是 (2)=CJm(2)+DNm(2) 1 d/d ." (x)=0的解是 y(a)=cjm(ic)+DNm(ic) ()+(m)-]R=0的解是 in丌 R(r)=CJm + DN
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 1 z d dz z dw dz + 1 − m2 z 2 w(z) = 0)´ w(z) = CJm(z) + DNm(z) 1 x d dx x dy dx + −1 − m2 x 2 y(x) = 0)´ y(x) = CJm(ix) + DNm(ix) 1 r d dr r dR dr + − nπ h 2 − m2 r 2 R = 0)´ R(r) = CJm inπ h r + DNm inπ h r C. S. Wu 1ù μê(n)
Bessel Functions with °因为r是实变量,故得到的函数 In/t h Jm(ia) Nm ( 都是以纯虚数为宗量的柱函数 因为当x为纯虚数时,函数值也是复数 AF(k++1)(2(尖
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 Ïr´¢Cþ§¼ê Jm inπ h r Nm inπ h r Jm(ix) Nm(ix) Ñ´±XJêmþμê ÏxXJꧼê´Eê Jν(xe iπ/2 ) = X ∞ k=0 (−) k k!Γ (k + ν + 1) x 2 e iπ/2 2k+ν = eiπν/2X ∞ k=0 1 k!Γ (k + ν + 1) x 2 2k+ν C. S. Wu 1ù μê(n)
Bessel Functions with °因为r是实变量,故得到的函数 In/t N Nm(ia) 都是以纯虚数为宗量的柱函数 因为当x为纯虚数时,函数值也是复数 i/2 k!「(k+v+1) k=0 2k+v A(k+v+1)(2)(索
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 Ïr´¢Cþ§¼ê Jm inπ h r Nm inπ h r Jm(ix) Nm(ix) Ñ´±XJêmþμê ÏxXJꧼê´Eê Jν(xe iπ/2 ) = X ∞ k=0 (−) k k!Γ (k + ν + 1) x 2 e iπ/2 2k+ν = eiπν/2X ∞ k=0 1 k!Γ (k + ν + 1) x 2 2k+ν C. S. Wu 1ù μê(n)
讲授要点 ③虚宗量Beel函数 虚宗量 Bessel方程 虚宗量 Bessel函数 虚宗量Bese函数的渐近行为 半奇数阶Bese函数 士1/2阶 Bessel,函数 其他情形 ③球 Bessel函数 球 Bessel方程的解 球 Bessel函数 平面波按球面波展开
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 ùÇ: 1 JmþBessel¼ê JmþBessel§ JmþBessel¼ê JmþBessel¼êìC1 2 Ûê Bessel¼ê ±1/2 Bessel¼ê Ù¦/ 3 ¥Bessel¼ê ¥Bessel§) ¥Bessel¼ê ²¡ÅU¥¡ÅÐm C. S. Wu 1ù μê(n)