Residues

Use residues to evaluate integral of a trigonometric function (see attachment)

evaluating integrals using residue theory I

3 integals evaluated by means of the residue calculus in complex analysis

Taylor series representation and residue

Please see the attached file

evaluating real integrals using residue theory II

3 integrals evaluated using the residue calculus in complex analysis

evaluating integrals using residue theory III

3 integrals computed using the residue calculus

numbered terms

What is the fifth term in the following sequence? asubcript n =n+asubscript n-1. if a1 equals -2, for n greater than or equal to 2.

Jordan's Lemma

Please see the attachment

Harmonic function

Please see attached. --- Let (attached) be a function that is analytic and not constant throughtout a bounded domain (attached) and continuous (attached) on its boundary (here domain is an open connected set). Prove, by considering (attached) , that the component function (attached) has a minimum value in the compact regi ...continues

Integration of uniformly convergent series

Please see attached.

Removable singularity

(See attached file for full problem description) --- Let have an isolated singularity at and suppose that is bounded in some punctured neighborhood of . Prove directly from the integral formula for the Laurent coefficients that for all j = 1,2,3,..., i.e. must have a removable singularity at . The integ ...continues