Über asymptotische Erzeugende rekursiv definierter Funktionen
To an arbitrary sequence of real functions a so-called asymptotic generating function is associated. This is a function possessing an asymptotic power series the coefficients of which are the given sequence of functions. Using a theorem of Ritt in the theory of asymptotic power series, it is shown that this always is possible. In the case where the sequence is recursively defined the asymptotic generating function turns out as a solution to a specific equation which may be a linear algebraic equation, ordinary difference equation of first order or partial differential equations of first or second order. A lot of special functions are covered by this method.
scientific article; zbMATH DE number 4046146