Page 44 - Calculus with Complex Numbers
P. 44

Find the Laurent expansions of the following functions at the points indicated.
        State what type of singularity each one is and what the residues are. lndicate
        the principal part in each case.

        (i) cZ;/z10 at c = 0,  (ii) sin z/z15 at c = 0,

        Find constants .4, B such that
                  3.: + 1      .4     B
        flz) = (           =       +      .
                z + 2)(z - 3)  z + 2  z - 3
        Hence lind the Maclatlrin expansion of flz) . What is its range of validity?
   39   40   41   42   43   44   45   46   47   48   49