By Nanny Fröman, Per Olof Fröman (auth.)
The potency of the phase-integral process constructed via the current au thors has been proven either analytically and numerically in lots of publica tions. With the inclusion of supplementary amounts, heavily on the topic of new Stokes constants and got using comparability equation approach, vital sessions of difficulties during which transition issues could process one another develop into obtainable to exact analytical therapy. The exposition during this monograph is of a mathematical nature yet has vital actual functions, a few examples of that are present in the adjoined papers. therefore, we wish to stress that, even supposing we target at mathematical rigor, our therapy is made basically with actual wishes in brain. To introduce the reader into the historical past of this publication, we begin by way of de scribing the phase-integral approximation of arbitrary order generated from an unspecified base functionality. this can be performed in bankruptcy 1, that's reprinted, after minor adjustments, from a evaluation article. bankruptcy 2 is the results of re seek paintings that was once pursued in the course of greater than 20 years, interrupted now and then. It begun within the sixties, once we have been nonetheless utilizing a phase-integral approximation, which in our current terminology corresponds to a different collection of the bottom functionality. on the time our basic objective was once to derive expressions for the supplementary amounts wanted that allows you to receive a correct connection formulation for a true capability barrier, whilst the strength lies locally of the pinnacle of the barrier.