and at this point it remains only to let n tend to infinity
in (32) to prove (29), which was a rewriting of (23).
The interpretation of the solution (14) is also complicated by the fact that it is defined on the semi-axis 0 < x < [infinity], at the boundaries of which either the amplitude A(x) or the phase [PSI](x) tend to infinity
max] [right arrow] [infinity] and [beta](n) eigenvalues tend to infinity
, with [beta](n) [right arrow] [infinity] for n [right arrow] [infinity].
Several authors (6) believes that it is not physically possible for the extensional viscosity to tend to infinity for a finite value of extensional rate.
Thus our model does not necessarily imply that the extensional viscosity will tend to infinity for a finite extensional rate for all polymer solutions.
3 these quotients tend to zero if at least two side lengths of the bounding box tend to infinity.
1 If at least two of r, s, t tend to infinity, the family
The rhs tends to zero for any fixed real x if r and s tend to infinity.
3) bounded from above by some fixed constant on some semicircles, whose radii tend to infinity
2][multiplied by]H([Tau]) tend to infinity
when [Tau] tends respectively to 0 and infinity.
n] tend to infinity as n [arrow right] [infinity], and consequently all informative characteristics of the asymptotic distribution of the zeros gets lost during the process.
As in the case of Taylor polynomials, one would like to know more about the specific manner in which poles and zeros of the Pade approximants tend to infinity.