令x=1,y=0得: 4f(1)f(0)=2f(1)f(0)=2*1/4=1/2令 y=1得 f(x)=f(x+1)+f(x-1) f(x-1)=f(x)+f(x-2)上面2式相加得 f(x+1)+f(x-2)=0f(x-2)+f(x-5)=0f(x+1)=f(x-5)f(x)周期为6f(2010)=f(6*335)=f(0)=1/2
2010F