- #1
nhrock3
- 403
- 0
i need to calculate this integral f(z)=\frac{z}{e^{2\pi iz^2}-1}\\
in this area
\gamma _r=\left \{ |z|=r \right \},r>2
i need to find the points which turn to zero in the denominator
and non zero in the numerator.
i got two such points
z=\pm \sqrt{n}
by using this formula
res(\sqrt{a})=\frac{p(a)}{q(a)'}
res(\sqrt{n})=\frac{1}{4\pi i}
res(-\sqrt{n})=\frac{1}{4\pi i}
the third point is z=0 but for it we have both numerator and denominator 0
i calculated the residium for it by res(f(x),a)=\lim_{x->a}(f(x)(x-a)) formula
but then
my prof says some stuff that involves the area
he says that my points are 0 +1 -1 +2^(0.5) -2^(0.5) etc.. because the denominator goes to zero
for each point have a residiu and i need to sum the residiums inside.
but here the area is not defined
its not like (by radius 3)
i don't know what point are inside the area
??
in this area
\gamma _r=\left \{ |z|=r \right \},r>2
i need to find the points which turn to zero in the denominator
and non zero in the numerator.
i got two such points
z=\pm \sqrt{n}
by using this formula
res(\sqrt{a})=\frac{p(a)}{q(a)'}
res(\sqrt{n})=\frac{1}{4\pi i}
res(-\sqrt{n})=\frac{1}{4\pi i}
the third point is z=0 but for it we have both numerator and denominator 0
i calculated the residium for it by res(f(x),a)=\lim_{x->a}(f(x)(x-a)) formula
but then
my prof says some stuff that involves the area
he says that my points are 0 +1 -1 +2^(0.5) -2^(0.5) etc.. because the denominator goes to zero
for each point have a residiu and i need to sum the residiums inside.
but here the area is not defined
its not like (by radius 3)
i don't know what point are inside the area
??
