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A Tauberian Theorem for a Scale of Logarithmic Methods of Summation

  • R. Phillips (a1)

Extract

We suppose throughout that p is a non-negative integer, and use the following notations:

where (n = 0 , 1 , 2 , … );

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References

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1. Agnew, R. P., Abel transforms and partial sums of Tauberian series, Ann. of Math. 50 (1949), 110117.
2. Borwein, D., A logarithmic method of summability, J. London Math. Soc. 83 (1958), 212220.
3. Borwein, D., On methods of summability based on power series, Proc. Roy. Soc. Edinburgh Sect. A 64 (1957), 342349.
4. Hardy, G. H., Divergent series (Oxford University Press, Oxford, 1949).
5. Ishiguro, K., Tauberian theorems concerning the summability methods of logarithmic type, Proc. Japan Acad. 39 (1963), 156159.
6. Ishiguro, K., A converse theorem on the summability methods, Proc. Japan Acad. 39 (1963), 3841.
7. Kwee, B., A Tauberian theorem for the logarithmic method of summation, Proc. Cambridge Philos. Soc. 63 (1967), 401405.
8. Pitt, H. R., Tauberian theorems (Bombay, 1958).
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A Tauberian Theorem for a Scale of Logarithmic Methods of Summation

  • R. Phillips (a1)

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