用傅里叶级数展开:
sin(x)=x-x^3/3!+x^5/5!-x^7/7!+...
sinc(x)=sin(pi*x)/(pi*x)
=[(pi*x)-(pi*x)^3/3!+(pi*x)^5/5!-(pi*x)^7/7!+...]/(pi*x)
=1-(pi*x)^2/3!+(pi*x)^4/5!-(pi*x)^6/7!+...
所以x→0时,lim sinc(x) = 1
x=0,cx=0,
sincx=sin0=0
把x=o代入,sin0=0
x趋近于0时,sinx约等于x,所以sinc0=1