Some Theorems Connected with Abel's Theorem on the Continuity of Power Series

G. H. Hardy

Type: Article

Publication Date: 1907-01-01

Citations: 11

DOI: https://doi.org/10.1112/plms/s2-4.1.247

Abstract

We may suppose either that/,, is a complex function of a real variable, or a function of a complex variable ; in the latter case the interval (0, 1) must be replaced by a region.

Locations

Proceedings of the London Mathematical Society - View
Zenodo (CERN European Organization for Nuclear Research) - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Some Extensions to Multiple Series of Abel's Theorem on the Continuity of Power Series	1905	T. J. I’A. Bromwich G. H. Hardy
+ PDF Chat	A General Theorem Concerning Absolutely Convergent Series	1904	G. H. Hardy
+ PDF Chat	Theorems Connected with Maclaurin's Test for the Convergence of Series	1911	G. H. Hardy
+	Extension to Other Series of Abel's and Tauber's Theorems on Power Series	1926	Alfred Kienast
+	A Theorem Concerning Power Series	1914	Harald Bohr
+ PDF Chat	An Extension of a Theorem on Oscillating Series	1913	G. H. Hardy
+	Where did the examples of Abel's continuity theorem go?	2020	Sergio A. Carrillo
+	Theorems Concerning Cesàro Means of Power Series	1934	G. H. Hardy J. E. Littlewood
+	Abel's Theorem and its Converse (II)	1924	G. H. Hardy J. E. Littlewood
+	On Some Identities Relating to Hardy's Convergence Theorem	1928	Karl Grandjot
+	Note on Lebesgue's Constants in the Theory of Fourier Series	1942	G. H. Hardy
+	Note on the Converse of Abel's Continuity Theorem	1925	A. E. Ingham
+	Notes on the Theory of Series (XVII) : Some New Convergence Criteria for Fourier Series	1932	G. H. Hardy J. E. Littlewood
+ PDF Chat	A Note on the Continuity or Discontinuity of a Function Defined by an Infinite Product	1909	G. H. Hardy
+ PDF Chat	Abel's Theorem and its Converse	1920	G. H. Hardy J. E. Littlewood
+	Some Theorems Concerning Trigonometrical Series of a Special Type	1931	G. H. Hardy
+	Notes on the Theory of Series (X) : Some More Inequalities	1928	G. H. Hardy J. E. Littlewood
+ PDF Chat	The Converse of Abel's Theorem on Power Series	1911	J. E. Littlewood
+	Notes on the Theory of Series (XII): On Certain Inequalities Connected with the Calculus of Variations	1930	G. H. Hardy J. E. Littlewood
+	Note on a Power Series Considered By Hardy and Littlewood	1929	Einar Hille

Works That Cite This (11)

Action	Title	Year	Authors
+	H	1989	Michiel Hazewinkel
+	Godfrey Harold Hardy	1950	E. C. Titchmarsh
+ PDF Chat	Essai d'une bibliographie de la représentation analytique d'une fonction monogène	1929	Einar Hille
+ PDF Chat	Sur les valeurs limites de moyennes de Cesàro et de Hölder	1929	Silvio Dobrowolski
+ PDF Chat	Sur la continuité des fonctions analytiques	1929	W. Fédoroff
+ PDF Chat	Estensione dei teoremi di Abel, Cesàro e Frobenius sulle serie di potenze, I e II.	1929	Gaspare Mignosi
+ PDF Chat	Contribution à la théorie des séries sommables par la méthode de Cesaro-Hölder. [Résumé?]	1929	A. Maksymowicz
+ PDF Chat	Über asymptotische Entwicklungen von Funktionen	1929	A. Haar
+ PDF Chat	Essai d'une bibliographie de la représentation analytique d'une fonction monogène	1929	Einar Hille
+ PDF Chat	Sur la relation du procédé de sommation de Cesàro et celui de Riemann	1929	A. Rajchman A. Zygmund

Works Cited by This (0)

Action	Title	Year	Authors