An extension of Mercer’s theorem
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- by R. T. Leslie and E. R. Love PDF
- Proc. Amer. Math. Soc. 3 (1952), 448-457 Request permission
References
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J. Mercer, On the limits of real variants, Proc. London Math. Soc. (2) vol. 5 (1907) pp. 206-224.
G. H. Hardy, Generalisations of a limit theorem of Mr. Mercer, Quart. J. Math. vol. 18 (1912) pp. 143-150.
T. Vijayaraghavan, A generalisation of the theorem of Mercer, J. London Math. Soc. vol. 3 (1928) pp. 130-134.
E. T. Copson and W. L. Ferrar, Notes on the structure of sequences, J. London, Math. Soc. vol. 4 (1929) pp. 258-264 and vol. 5 (1930) pp. 21-27.
- Wallie Abraham Hurwitz, The Oscillation of a Sequence, Amer. J. Math. 52 (1930), no. 3, 611–616. MR 1506778, DOI 10.2307/2370629 R. P. Agnew, On equivalence of methods of evaluation of sequences, Tôhoku Math. J. vol. 35 (1932) pp. 244-252. J. Karamata, Sur quelques inversions d’une proposition de Cauchy, Tôhoku Math. J. vol. 36 (1933) pp. 22-28. H. R. Pitt, Mercerian theorems, Proc. Cambridge Philos. Soc. vol. 34 (1938) pp. 510-520.
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- G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620 E. R. Love, Mercer’s summability theorem, accepted for publication in J. London Math. Soc.
Additional Information
- © Copyright 1952 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 3 (1952), 448-457
- MSC: Primary 40.0X
- DOI: https://doi.org/10.1090/S0002-9939-1952-0047159-6
- MathSciNet review: 0047159