User:Mwomath

In 1947, E. Lindel¨of gives his contribution to study how someone can use the residue theory to evaluate infinte series. In his paper :Le calcul Des R´esidus et Ses Applications `a la Th´eorie Des Fonctions, he was give a brief about this subject.

In 2007, M. Alomari gives another approach to this subject, the method(s) that devoted by him is : New Method to Evaluate Certain Classes of Infinite Series by Analytic Functions, he established a very useful ideas by using the meromorphic function in the finite plane to relate the method that devoted by Lindel¨of.

The summary of his contribution about this subject is to study some of a problem(s) about the evaluation of infinite series as well as infinite products using residue theory.

In general the behavior of the meromorphic function in the finite and extended plane is studied in such that : how a meromorphic function behave near removable singularity and near poles.

He also discussed the behavior of an analytic function near essential singularity and relate it with the meromorphic function in finite and extended plane, and thus he obtain a very strong relation between them by some results (related with the analytic function) which are needed to evaluate infinite sums as well as infinite products by residues.