f(-∞,-∞)=a(b-π/2)(c-π/2)=0
f(-∞,+∞)=a(b-π/2)(c+π/2)=0
f(+∞,-∞)=a(b+π/2)(c-π/2)=0
f(+∞,+∞)=a(b+π/2)(c+π/2)=1
解得:a=1/π^2,b=π/2,c=π/2
f(x,y)=df(x,y)/dxdy=1/[π^2
(1+x^2)(1+y^2)]
边缘函数
fx(x)=∫f(x,y)dy
从负无穷积分到正无穷
=1/[π(1+x^2)]
fy(y)=∫f(x,y)dx
从负无穷积分到正无穷
=1/[π(1+y^2)]