Learn Polish: Kupiłem publikację zawierającą szczegółową analizę tego zjawiska. - I bought a publication containing a detailed analysis of this phenomenon.

The word zawierającą is an active adjectival participle meaning "containing". It acts as a syntactic shortcut to replace the relative clause która zawiera (which contains). Because it behaves like an adjective, it must agree with the noun it modifies (publikację), taking the feminine accusative singular form.

Could I use a perfective verb to form the participle zawierającą if I wanted to?

No, active adjectival participles (the ones ending in -ący, -ąca, -ące) can only be formed from imperfective verbs like zawierać. You cannot form this type of participle from a perfective verb. If you need to express a completed action, you must use a standard relative clause with który instead of a participle.

Why is szczegółową analizę in the accusative case if it follows an adjective-like word?

Although zawierającą takes adjective endings to match publikację, it still acts like a verb underneath. The verb zawierać (to contain) requires a direct object in the accusative case, so its participle form also forces the following phrase szczegółową analizę into the accusative.

Why do we use the genitive case for tego zjawiska?

It is in the genitive case because it translates the English "of" in "analysis of this phenomenon". When one noun modifies another noun to show a relationship or possession, the second noun takes the genitive case in Polish.