We present a new integral transform called the generalized Borel transform (GBT) and show how to use it to compute distribution functions used to describe the statistical mechanics of macromolecules. For this purpose, we choose the random flight model (RFM) of macromolecules and show that the application of the GBT to this model leads to the exact expression of the polymer propagator (two-point correlation function) from which all the statistical properties of the model can be obtained. We also discuss the mathematical simplicity of the GBT and its applicability to macromolecules with other topologies. (C) 2003 American Institute of Physics.