Homework Statement
Let u(z) be a continuous function from D to [-inf, inf) (In the extended field sense which includes -inf). Suppose u_n (z) is a decreasing sequence of subharmonic functions on D such that u_n converges to a function v pointwisely. Show that v(z) is subharmonic.
Homework...
say you have a function f(z) with all the desired poles, and another function g(z) with desired zeros, since both poles are zeros are distinct, a function f(z)g(z) will be a meromorphic function with both desired poles and zeros.
Now the problem is that singular part(s) in f(z) is no longer...
Homework Statement
Let G be a region and let {a_n} and {b_m} be two sequences of distinct points in G such that a_n != b_m for all n,m. Let S_n(z) be a singular part at a_n and let p_m be a positive integer. Show that there is a meromorphic function f on G whose only poles and zeros are...
1. is to solve the equation, means to get the x, and I have no clue...
2.I think it's solvable, thus I used hensel lemma and got f'(x)=2x with |f(x)|_7... but haven't got a number which can satisfy the equation
3. for n+1, up to n^2 there will be n^2+1, and minus the n one in p^n, thus u...