15.3 Suppose that {n} is a sequence of distinct points in D(0; 1) such that n0...

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15.3 Suppose that {n} is a sequence of distinct points in D(0; 1) such that n0 as n. Decide whether the following statements are true for all choices of {n}. (i) If f is holomorphic in D(0; 1) and f(n) f(z) = sin for all z D(0; 1). = sin zn for all n, then (ii) There exists f = D(0; 1) such that f(n) = n for all n. (iii) There exists f = D(0; 1) such that f(n) such that f(n) = zn when n is odd. = O when n is even and (iv) There exists f = D(0; 1) which is such that f(zn) = (1)"zn for every n. Justify your answers. 15.3 Suppose that {n} is a sequence of distinct points in D(0; 1) such that n0 as n. Decide whether the following statements are true for all choices of {n}. (i) If f is holomorphic in D(0; 1) and f(n) f(z) = sin for all z D(0; 1). = sin zn for all n, then (ii) There exists f = D(0; 1) such that f(n) = n for all n. (iii) There exists f = D(0; 1) such that f(n) such that f(n) = zn when n is odd. = O when n is even and (iv) There exists f = D(0; 1) which is such that f(zn) = (1)"zn for every n. Justify your answers.