Some analogies in analysis

One of the most common methods of scientific research is analogy. Analogy is the transfer of knowledge to a higher level, based on the creation of common characteristics or interrelationships of these things. The use of analogy is associated with the transformation of ideas, with mental experiences, that is, with the independent expansion and deepening of existing knowledge. The purpose of this work is to identify analogies in improper integrals and number series.