Bessel Functions with 定义 1(x)=e -iv/2 ∑ k!「(k++1) 称为第一类虚宗量 Bessel函数 相应地,方程 称为虚宗量Bese方程
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 ½Â Iν(x) = e−iπν/2 Jν(xe iπ/2 ) = X ∞ k=0 1 k!Γ (k + ν + 1) x 2 2k+ν ¡1aJmþBessel¼ê A/§§ 1 x d dx x dy dx + −1 − ν 2 x 2 y(x) = 0 ¡JmþBessel§ C. S. Wu 1ù μê(n)
Bessel Functions with 定义 1(x)=e -iv/2 ∑ k!「(k++1) 称为第一类虚宗量 Bessel函数 相应地,方程 2(出)+(1-2) 称为虚宗量 Bessel方程 C. S. Wu
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 ½Â Iν(x) = e−iπν/2 Jν(xe iπ/2 ) = X ∞ k=0 1 k!Γ (k + ν + 1) x 2 2k+ν ¡1aJmþBessel¼ê A/§§ 1 x d dx x dy dx + −1 − ν 2 x 2 y(x) = 0 ¡JmþBessel§ C. S. Wu 1ù μê(n)
Bessel Functions with 当≠整数时,虚宗量 Bessel方程 1 d d d y(x)=0 的解l士(x)线性无关 当=整数n时,1(x)线性相关 J(x)=1(x)
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 ν 6=ê§JmþBessel§ 1 x d dx x dy dx + −1 − ν 2 x 2 y(x) = 0 )I±ν(x)5Ã' ν =ên§I±n(x)5' I−n(x) = in J−n(ix) = (−i)n Jn(x) = i−n Jn(x) = In(x) C. S. Wu 1ù μê(n)
Bessel Functions with 当≠整数时,虚宗量 Bessel方程 1 d d d y(x)=0 的解l士(x)线性无关 当=整数n时,ln(x)线性相关 ()=inU-n(ic)=iJn(a) =i Jn(=In(a)
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 ν 6=ê§JmþBessel§ 1 x d dx x dy dx + −1 − ν 2 x 2 y(x) = 0 )I±ν(x)5Ã' ν =ên§I±n(x)5' I−n(x) = in J−n(ix) = (−i)n Jn(x) = i−n Jn(x) = In(x) C. S. Wu 1ù μê(n)
Bessel Functions with 虚宗量 Bessel方程 1 d/ d +(-1 (x)=0 的第二解也可取为 第二类虚宗量 Bessel函数( McDonald函数 K()=20[L()-b() Kn(x)仍然有意义,且与(x)线性无关 (a)- lim K,( 2sIn TL
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 JmþBessel§ 1 x d dx x dy dx + −1 − ν 2 x 2 y(x) = 0 1) 1aJmþBessel¼ê(McDonald¼ê) Kν(x) = π 2 sin νπ h I−ν(x) − Iν(x) i Kn(x)E,k¿Â§ In(x)5Ã' Kn(x) = lim ν→n Kν(x) = lim ν→n π 2 sin νπ h I−ν(x) − Iν(x) i C. S. Wu 1ù μê(n)