Polynomial Hamiltonians associated with Painlevé equations, I

The purpose of this.note is. to study Hamiltn- ians associated with the six equations, of Painlev, and r-functions related to Hamiltonians.The Painlev equations are given by the fol- lowing table" Piv ,,-(2,y.+ 3 + 4t.+ 2(t-_ a) + ] 2 (-1 )(ZY-I'+ Pv 2"= + 2--I t (]--1)t (+)+i] + (]+--II) 1(1 1..+ 1 =-7 + I--1 i 1 Y+ t--1 i--t + ](]--1)(]--t) [a+ t t(t ly