1.Let be positive integer and
be an odd positive integer.Find the highest power of 2 which divides {\large
.}
2.Let be two complex numbers which are linearly independent over
.Conside the lattice
generated over
Show that the Weirestrass elliptic function{\large } is absolutely and uniformly convergent on any compact subset of the complex plane which doesn’t contain any points of
.Also,show that
is meromorphic with a double pole only at points in
.
3.The deleted infinite broom is the set of all line segments joining
to
and the point
.Note that the segment between
and
through the X-axis is not included.
Prove that the deleted infinite broom is connected but not path-connected.
The closure of the deleted infinite broom is called the infinite broom.Prove that the infinite broom is path-connected.
4.Show that the roots of Legendre Polynomial in the interval are distinct.