Polynomials with complex roots-holomorphic functions

Reference no: EM13122060

Let C be a circle enclosing the distinct points z1,z2,...zn. Let p(z)=(z-z1)(z-z2)...(z-zn) be the polynomial of degree n with roots at these points. Let f(z) be holomorphic in a disc that includes C. Show that P(z)=1/i2pi(integral over C of (f(w)/p(w)[(p(w)-p(z)/w-z)]dw) is a polynomial of degree n-1, with the property P(z_i)=f(z_i), i=1,2,..n

Reference no: EM13122060

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