A simple closed path C in the complex plane is shown in the figure. If

$$\oint\limits_c {{{{2^z}} \over {{z^2} - 1}}dz = - i\pi A} $$,

where $$i = \sqrt { - 1} $$, then the value of A is ___________ (rounded off to two decimal places).

Consider the following series:

$$\sum\limits_{n = 1}^\infty {{{{n^d}} \over {{c^n}}}} $$

For which of the following combinations of c, d values does this series converge?

The residues of a function $$f\left( z \right) = {1 \over {\left( {z - 4} \right){{\left( {z + 1} \right)}^3}}}$$ are

For $$f\left( z \right) = {{\sin \left( z \right)} \over {{z^2}}},$$ the residue of the pole at $$z=0$$ ________.