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We extend to the setting of Dirichlet series previous results of H. Bohr for Taylor series in one variable, themselves generalized by V. I. Paulsen, G. Popescu and D. Singh or extended to several variables by L. Aizenberg, R. P. Boas and D. Khavinson. We show in particular that, if $f (s) = \sum_{n = 1}^{\infty} a ₙ n^{- s}$ with ${| | f | |}_{\infty} : = s u p_{ℜ s > 0} | f (s) | < \infty$ , then $\sum_{n = 1}^{\infty} | a ₙ | n^{- 2} {\leq | | f | |}_{\infty}$ and even slightly better, and $\sum_{n = 1}^{\infty} | a ₙ | n^{- 1 / 2} {\leq C | | f | |}_{\infty}$ , C being an absolute constant.

The coefficients of the Laurent expansion of analytic functions

Alexander Abian (1977)

Archivum Mathematicum

The generalized monotonicity class and integrability of power series

Sergey Volosivets, Valery Krivobok (2013)

Colloquium Mathematicae

The aim of this paper is to obtain a generalization of W. A. Woyczyński and B. Ram results concerning integrability of power series in terms of their coefficients for the class GM of general monotonic sequences.

The generalized weighted probability measure on the symmetric group and the asymptotic behavior of the cycles

Ashkan Nikeghbali, Dirk Zeindler (2013)

Annales de l'I.H.P. Probabilités et statistiques

The goal of this paper is to analyse the asymptotic behaviour of the cycle process and the total number of cycles of weighted and generalized weighted random permutations which are relevant models in physics and which extend the Ewens measure. We combine tools from combinatorics and complex analysis (e.g. singularity analysis of generating functions) to prove that under some analytic conditions (on relevant generating functions) the cycle process converges to a vector of independent Poisson variables...

The maximum term of a power series.

Srivastava, G.S., Juneja, O.P. (1986)

International Journal of Mathematics and Mathematical Sciences

The remainder term of the Taylor expansion for a holomorphic function is representable in Lagrange form.

Radzievskaya, E.I., Radzievskij, G.V. (2003)

Sibirskij Matematicheskij Zhurnal

The Taylor series and growth of means.

Earl Berkson (1983)

Journal für die reine und angewandte Mathematik

The value-distribution of lacunary series and a conjecture of Paley

Takafumi Murai (1981)

Annales de l'institut Fourier

The purpose of this paper is to establish a theorem which answers a conjecture of Paley on the distribution of values of Hadamard lacunary series and which is useful to study the Peano curve property of such series.

Théorèmes généraux sur les points singuliers des fonctions données par une série de Taylor

L. Desaint (1902)

Journal de Mathématiques Pures et Appliquées

Theorems on the Convergence of Series in Generalized Lommel-Wright Functions

Paneva-Konovska, Jordanka (2007)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20The classical Cauchy-Hadamard, Abel and Tauber theorems provide useful information on the convergence of the power series in complex plane. In this paper we prove analogous theorems for series in the generalized Lommel-Wright functions with 4 indices. Results for interesting special cases of series involving Bessel, Bessel-Maitland, Lommel and Struve functions, are derived.We provide also a new asymptotic formula for the generalized ...

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Sur un algorithme algébrique

Sur un mode de développement en série des fonctions algébriques explicites

Sur une classe de fonctions non uniformes

Taylor Series of the Natural Powers of the Pick Function and Applications

The analytic fixed point function. II.

The Bohr inequality for ordinary Dirichlet series

The coefficients of the Laurent expansion of analytic functions

The generalized monotonicity class and integrability of power series

The generalized weighted probability measure on the symmetric group and the asymptotic behavior of the cycles

The maximum term of a power series.

The remainder term of the Taylor expansion for a holomorphic function is representable in Lagrange form.

The Taylor series and growth of means.

The value-distribution of lacunary series and a conjecture of Paley

Théorèmes généraux sur les points singuliers des fonctions données par une série de Taylor

Theorems on the Convergence of Series in Generalized Lommel-Wright Functions

Über die Fortsetzung analytischer Funktionen.

Über die Koeffizientensummen einiger Klassen von Potenzreihen

Über eine Defekt- und Verzweigungsrelation für die Ableitung meromorpher Funktionen.

Über eine Fragestellung von Gaier und Meyer-König.

Über gewisse nichtfortsetzbare Potenzreihen.

Currently displaying 121 – 140 of 169