The problem of determining of the normalization constant of a wave function describing an arbitrary type of an infinite motion for a one-dimensional potential is discussed. It is shown that for the cases of the momentum or the quasi-wave number representations the normalization constant does not depend on the representation parameter. In contrast to these cases for the energy representation the...

A perturbation scheme is discussed for the computation of the normalization constant of the large order behavior arising from an ultraviolet renormalon. In this scheme the normalization constant is expressed in a convergent series that can be calculated using the ordinary perturbative expansion and the nature of the renormalon singularity. PACS numbers: 11.15.Bt, 11.10.Jj, 11.25.Db

For convex hypersurfaces in the affine space $\mathbb{A}^{n+1}$ ($n\geq2$), A.-M.\ Li introduced notion of $\alpha$-normal field as a generalization normal field. By studying Monge-Amp\`ere equation with gradient blowup boundary condition, we show that regular domains $\mathbb{A}^{n+1}$, defined respect to proper cone and satisfying some regularity assumption if $n\geq3$, are foliated by comple...

By adding a second parameter, Conway and Maxwell created a new distribution for situations where data deviate from the standard Poisson distribution. This new distribution contains a normalization constant expressed as an infinite sum whose summation has no known closed-form expression. Shmueli et al. produced an approximation for this sum but proved only that it was valid for integer values of...