I've often heard folks ask either what the Jesus Prayer is, or what formula is repeated. The most common formula for the Jesus Prayer is "Lord Jesus Christ, Son of God, have mercy on me a sinner." But is that the only formula? Is that the Jesus Prayer? The answer is a resounding "no!"
There are actually three formulas today which are most common. The shortest is "Lord Jesus Christ, have mercy on me." The one used on Mt. Athos is "Lord Jesus Christ, Son of God, have mercy on me." This latter is also the oldest "official" form of the Jesus Prayer. The words "a/the sinner" were later added on to this formula through Russian piety. St. Ignatius Brianchaninov considered the addition of those words to be the crowning perfection of the already perfect Jesus Prayer (check out his book On the Prayer of Jesus).
But historically the Jesus Prayer simply referred to the invocation of the name of Jesus. Fr. Lev Gillet (aka "A Monk of the Eastern Chruch") in his marvelous little book The Jesus Prayer emphasizes that historically the Jesus Pray had an almost innumerable amount of forms, ranging anywhere from a simple and devout repetition of the name "Jesus" to the longer, more elaborate formulas. In his Byzantine Daily Worship Archbishop Joseph Raya provides the formula "Lord Jesus, Son of God, have mercy on me a sinner," but in another of his works (Christmas: Birth of Our Lord God and Saviour Jesus Christ) he suggests "Jesus, Son of the living God, have mercy on me a sinner."
Archbishop Raya and other scholars suggests that the Jesus Prayer grew out of the short "ejaculatory" prayers that monks used to pray in order to focus their minds on God's presence (see, for example, Metropolitan Kallistos Ware's The Inner Kingdom). Prayers such as "God, come to my assistance, Lord make haste to help me," are frequently suggested for use in times of temptation by the fathers of the Philokalia. And monks, according to Raya, used to pray "Sweetest Jesus, glory of monks, save me, your servant," and "Sweetest Jesus, Philanthropos, have mercy on me."
This devotion was not limited to the East, but spread in many different forms in the West as well. Such prayers as "Jesus meek and humble of heart, make my heart like unto Thine" can, in fact, be considered Western forms of the Jesus Prayer. I remember one particular priest-friend of mine growing up. During the elevation of the consecrated Host at Mass he always used to say, "My Jesus, mercy." Inspired by his example I used to repeat the same. This was probably my first form of the Jesus Prayer.
St. Theophan the Recluse tells us that the formula of the Jesus Prayer is not important because the formula itself derives its power from the name of Jesus. So, when praying the Jesus Prayer, don't get caught up in what is the "correct" formula. Simply find a version that best helps you to focus your mind on the presence of God in your heart, then stick with it.