On the circle method of summation of a Cauchy product series

On the circle method of summation of a Cauchy product series
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by Kazuo Ishiguro PDF

Proc. Amer. Math. Soc. 13 (1962), 695-697 Request permission

References

Konrad Knopp, Über das Eulersche Summierungsverfahren, Math. Z. 18 (1923), no. 1, 125–156 (German). MR 1544625, DOI 10.1007/BF01192401
G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620
Hisao Hara, On the Cauchy’s product series theorem on Euler’s summability, K\B{o}dai Math. Sem. Rep. 5 (1953), 91–92. {Volume numbers not printed on issues until Vol. 7 (1955)}. MR 57991
W. Meyer-König, Untersuchungen über einige verwandte Limitierungsverfahren, Math. Z. 52 (1949), 257–304 (German). MR 32021, DOI 10.1007/BF02230694
P. Vermes, Series to series transformations and analytic continuation by matrix methods, Amer. J. Math. 71 (1949), 541–562. MR 30015, DOI 10.2307/2372347
P. Vermes, The transpose of a summability matrix, Colloque sur la théorie des suites, tenu à Bruxelles du 18 au 20 décembre 1957, Centre Belge de Recherches Mathématiques, Librairie Gauthier-Villars, Paris; Établissements Ceuterick, Louvain, 1958, pp. 60–86. MR 0100735
M. S. Ramanujan, Series-to-series quasi-Hausdorff transformations, J. Indian Math. Soc. (N.S.) 17 (1953), 47–53. MR 56723
M. S. Ramanujan, A note on the quasi-Hausdorff series-to-series transformations, J. London Math. Soc. 32 (1957), 27–32. MR 83603, DOI 10.1112/jlms/s1-32.1.27
Kazuo Ishiguro, Zur Gibbsschen Erscheinung für das Kreisverfahren, Math. Z. 76 (1961), 288–294 (German). MR 132351, DOI 10.1007/BF01210979