This is the 9268th most frequent Russian word.
специальную
"Special" or "specialized" (feminine singular accusative form in Russian).
The word 'специальную' (a form of 'special') describes a book tailored for a specific purpose, here for studying mathematics.
Она купила специальную книгу для изучения математики.
She bought a special book for studying mathematics.
Here, 'специальную' refers to a room that has been designated specifically for guest use.
Мы выделили специальную комнату для гостей.
We allocated a special room for guests.
In this sentence, 'специальную' is used to describe a methodology crafted specifically for conducting the mentioned research.