  The well-known algorithm for summing of divergent series is based on the
Borel transformation in combination with the conformal mapping (Le Guillou and
Zinn-Justin, 1977). Modification of this algorithm allows to determine a strong
coupling asymptotics of the sum of the series through the values of the
expansion coefficients. Application of the algorithm to the \beta-function of
\phi^4 theory leads to the asymptotics \beta(g)=\beta_\infty g^\alpha at
g\to\infty, where \alpha\approx 1 for space dimensions d=2,3,4. The natural
hypothesis arises, that asymptotic behavior is \beta(g)\sim g for all d.
Consideration of the "toy" zero-dimensional model confirms the hypothesis and
reveals the origin of this result: it is related with a zero of a certain
functional integral. Generalization of this mechanism to the arbitrary space
dimensionality leads to the linear asymptotics of \beta(g) for all d. The same
idea can be applied for QED and gives asymptotics \beta(g)=g, where g is the
running fine structure constant. Relation to the "zero charge" problem is
discussed.
