●6函数,并不是通常意义下的函数:它并没有 给出函数与自变量之间的对应关系 它给出的对应关系 6(x) 当x≠0 当x=0 在通常意义下是没有意义的 它所给出的“函数值”只是在积分运算中才 有意义 f(a)8(a).c=f(O)
Dirac δ function Green Functions of ODE Possible Symmetric Properties of GF’s Density Distribution of A Point Source Basic Operation Rules 2D & 3D δ functions δ¼ê§¿Ø´Ï~¿Âe¼êµ§¿vk ѼêgCþméA'X §ÑéA'X δ(x) = ( 0 x 6= 0 ∞ x = 0 3Ï~¿Âe´vk¿Â §¤Ñ/¼ê0´3È©$¥â k¿Â Z ∞ −∞ f(x)δ(x)dx = f(0) C. S. Wu 1Êù δ¼ê
δ函数也可以理解为(任意阶可微)函数序列的 极限 凡是具有 性质的函数序列(x),或是具有 性质的画数序列(),它们的极限都是画美
Dirac δ function Green Functions of ODE Possible Symmetric Properties of GF’s Density Distribution of A Point Source Basic Operation Rules 2D & 3D δ functions δ¼ê±n)(?¿ )¼êS 4 ´äk lim l→0 Z ∞ −∞ f(x)δl(x)dx = f(0) 5¼êSδl(x)§½´äk lim n→∞ Z ∞ −∞ f(x)δn(x)dx = f(0) 5¼êSδn(x)§§4Ñ´δ¼ê C. S. Wu 1Êù δ¼ê
δ函数也可以理解为(任意阶可微)函数序列的 极限 凡是具有 lim/f(c)5(a)dz=f(O 性质的函数序列(x),或是具有 lim/f()on(z)dz=f(O) 性质的函数序列5(),它们的极限都是6函线
Dirac δ function Green Functions of ODE Possible Symmetric Properties of GF’s Density Distribution of A Point Source Basic Operation Rules 2D & 3D δ functions δ¼ê±n)(?¿ )¼êS 4 ´äk lim l→0 Z ∞ −∞ f(x)δl(x)dx = f(0) 5¼êSδl(x)§½´äk lim n→∞ Z ∞ −∞ f(x)δn(x)dx = f(0) 5¼êSδn(x)§§4Ñ´δ¼ê C. S. Wu 1Êù δ¼ê
例如(x)=lim 又如0(x)=m 尜
Dirac δ function Green Functions of ODE Possible Symmetric Properties of GF’s Density Distribution of A Point Source Basic Operation Rules 2D & 3D δ functions ~X δ(x) = lim n→∞ n √ π e −n 2x 2 qX δ(x) = lim n→∞ n π 1 1 + n2x 2 $k δ(x) = sin nx πx C. S. Wu 1Êù δ¼ê
例如6(x)=mye~n2 又如6(x)=imn-1 1+n2x2 sI n. 甚至有0(x)
Dirac δ function Green Functions of ODE Possible Symmetric Properties of GF’s Density Distribution of A Point Source Basic Operation Rules 2D & 3D δ functions ~X δ(x) = lim n→∞ n √ π e −n 2x 2 qX δ(x) = lim n→∞ n π 1 1 + n2x 2 $k δ(x) = sin nx πx C. S. Wu 1Êù δ¼ê