I do not understant how to prove the seconde question. Could you help me.
we have a in C, C is the set of complexe number, and b a complexe number, r>0 a real number. Let U=D(b,r)\{a}. We have f a holomorphic function on U and R(f(z))>=0, where R(f(z)) si the real part of the function f, for all z in U.
1. Show that bis not an essential singular point of f.
2.
Show that f extends into a holomorphic function over the entire disc D(b,r)
we have a in C, C is the set of complexe number, and b a complexe number, r>0 a real number. Let U=D(b,r)\{a}. We have f a holomorphic function on U and R(f(z))>=0, where R(f(z)) si the real part of the function f, for all z in U.
1. Show that bis not an essential singular point of f.
2.
Show that f extends into a holomorphic function over the entire disc D(b,r)