It is an investigative or contemplative concentration. Your brain is constantly calculating and analysing in this form of concentration. Think of a chess player. A chess player can look at the chessboards unblinking for very long periods. He is concentrating but it’s not one pointed concentration. He is constantly evaluating their line of attack, variations, moves and the opponent’s repossess. He is so absorbed in that analytical investigation that the world around him ceases to exist. Neither hunger, thirst not nature’s call, nothing disturbs him when they are calculating. If you play chess or if you ever had the opportunity to observe a chess player closely, you will know what I mean.
The ability to carry out penetrating analysis on any given line of thought results from analytical concentration. A computer programmer engrossed in fixing a bug or creating a new piece of software, or a mathematician working on a theorem, they are masters of analytical concentration. Some of the all time greatest scientists and inventors were extremely skilled in this type of concentration.
Like the other forms of concentration, the more you practice it, the better you get at it. It continues to sharpen. Over time, you are able to carry out even more detailed analysis quicker. That is not just because of experience in your field but also because your mind can cut through the noise and stay focused in the analysis.
Reference : Om Swami. A Million Thoughts.