This opening is unique in all of Paul's letters.
Nowhere else does Paul allow the co-sender's name to stand in apposition with his own next to the epithet he uses -- here, "servants." I gather from this that he was making a point. Some say he was lowering himself to Timothy's level. I like to think of it as Paul elevating Timothy to his. Both of them were equally servants of Christ. Both had worked as a team when ministering in Philippi. In fact, the ministry of all true Christians is to serve rather than be served. Moreover, as fellow servants of Christ, the relationships between believers is not one of superiority or inferiority but of "humble equality" (Collange).
Looking back over almost 5 decades of teaching, I am grateful beyond words for all those fellow servants of Christ alongside of whom I had the honor and joy of serving. "Partnership in the cause of the gospel" is an essential element of Christian unity and is, in fact, the theme of Philippians. Possessing a "common mind" that puts others first embraces not only the heart of Paul's message in Philippians but also in the whole of the New Testament. Gospel ministry is a common effort. All have a role to play. No one is in any way to be degraded for their lack of official status. Rather, all are to be valued and respected highly for their energetic cooperation with Paul, since they are working at his side as esteemed members of his team. No wonder Paul so strongly and adamantly appeals to the Philippians to cooperate with him now by resisting divisions and doing everything they can to restore harmony within the church.
This is what we are here for. Are you ready to pray, not "Lord, bless my ministry," but "Lord, bless our ministry"?