SUMMATION OF AN INFINITE SERIES OF LADDER DIAGRAMS

The recent result of Ussyukina and Davydychev, relating L-loop 3-point and 4-point ladder diagrams in 4-dimensional massless lambdaphi3/3! t heory, is derived from a conformal transformation. An expansion of the underlying integral is given in terms of Chebyshev polynomials. For t he sum of ladder contributions to the derivative of the self-energy, E uler-Maclaurin and Abel-Plana methods yield the strong-coupling expans ion SIGMA(lad)'(w2) approximately 1/24 - e-lambda/w (lambda/2piw)5/2 [ 1/2pi + 0 (w /lambda)], with a constant term -1/2zeta(-1) = 1/24 at in finite coupling and time-like momenta, which reflects the lack of a ze ro-loop perturbative contribution. The exponentially suppressed correc tions are obtained exactly, as a simple contour integral that yields a n asymptotic series.