On extensions of the Laurents' theorem in the fractional calculus with applications to the generation of higer transcendental functions
On extensions of the Mittag-Leffler theorem
The classical Mittag-Leffler theorem on meromorphic functions is extended to the case of functions and hyperfunctions belonging to the kernels of linear partial differential operators with constant coefficients.
On Fabry's gap theorem
By combining Turán’s proof of Fabry’s gap theorem with a gap theorem of P. Szüsz we obtain a gap theorem which is more general then both these theorems.
On folding solutions of the Beltrami equation.
On generalizations of the series of Taylor, Lagrange, Laurent and Teixeira.
On Kaluza's sign criterion for reciprocal power series
T. Kaluza has given a criterion for the signs of the power series of a function that is the reciprocal of another power series. In this note the sharpness of this condition is explored and various examples in terms of the Gaussian hypergeometric series are given. A criterion for the monotonicity of the quotient of two power series due to M. Biernacki and J. Krzyż is applied.
On lacunary analogs of the Poincaré theta-series and their applications.
On Lindelöf's error bound for Stirling's series.
On multi-dimensional generalizations of the Wiener-Żelazko and Lévy-Żelazko theorems
Multi-dimensional generalizations of the Wiener-Żelazko and Lévy-Żelazko theorems are obtained.
On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications
On quotients of holomorphic funtions in the dics with boundary regularity conditions.
In this paper we give characterizations of those holomorphic functions in the unit disc in the complex plane that can be written as a quotient of functions in A(D), A∞(D) or Λ1(D) with a nonvanishing denominator in D. As a consequence we prove that if f ∈ Λ1(D) does not vanish in D, then there exists g ∈ Λ1(D) which has the same zero set as f in Dbar and such that fg ∈ A∞(D).
On recurrence properties of certain lacunary series. I. General results.
On recurrence properties of certain lacunary series. II. General results.
On rules of derivation with complex order for analytic and branched functions
On series, integrals and continued fractions, III
On small divisors
On some combinatorial relations for Tornheim's double series
On the Analytic Continuation of Rank One Eisenstein Series.
On the Angular Derivative of Analytic Functions.
On the asymptotic boundary paths of analytic functions.