Explicit representation of structurally finite entire functions (Q5945217)

The author investigates a new relation for entire functions \(f, f_1, f_2\) which he describes as follows: \(f\) is constructed from \(f_1\) and \(f_2\) by Maskit surgery. The author gives the accurate definition of this relation.NEWLINENEWLINENEWLINEAn entire function is called a structurally finite entire function of type \((p,q)\) if it is constructed from \(p\) quadratic blocks of type \(az^2+bz+c\), \(a\neq 0\) and \(q\) exponential blocks of type \(a\exp(bz)+c\), \(ab\neq 0\). The author proves that the set of structurally finite entire functions of type \((p,q)\) coincides with the set of the form NEWLINE\[NEWLINE\int\limits_0^z(c_pt^p+\dots +c_0)e^{a_q t^q+\dots +a_0} dt+b,\;c_p a_q\neq 0.NEWLINE\]