Convergence Factors for Double Series Summable by Nörlund Means | Zendy

Charles N. Moore | Zendy

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Convergence Factors for Double Series Summable by Nörlund Means

Author(s) -

Charles N. Moore

Publication year - 1936

Publication title -

proceedings of the national academy of sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 5.011

H-Index - 771

eISSN - 1091-6490

pISSN - 0027-8424

DOI - 10.1073/pnas.22.3.167

Subject(s) - nucleic acid , small molecule , convergence (economics) , molecule , series (stratigraphy) , chemistry , nucleic acid structure , conformational change , biophysics , computational biology , computer science , biological system , biochemistry , biology , gene , rna , paleontology , organic chemistry , economics , economic growth

In a note' published in volume 21 of these PROCEEDINGS I gave necessary and sufficient conditions for convergence factors in simply infinite series summable by N6rlund means. The purpose of the present note is to furnish analogous results for double series. We are given a doubly infinite set of complex constants cij (i, j = 0, 1, 2, 3, .. .), where coo 0 0 and Zc,ix'y' is convergent for I x I < 1, I y I < 1, and becomes infinite as (x, y) approaches (1, 1) through real values. We set m n

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