Comparison of Raabe’s and Schlömilch’s tests

Franciszek Prus-Wiśniowski

doi:10.2478/v10127-009-0012-y

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Comparison of Raabe’s and Schlömilch’s tests

Tatra Mountains Mathematical Publications

Volume 42 (2009): Issue 1 (April 2009)

By: Franciszek Prus-Wiśniowski

Open Access

|Nov 2012

Abstract

The exact relationship between the Raabe’s test and Schl¨omilch’s test is described and a useful improved version of the divergence part of these tests is given. Furhter, a more general “continuous” scale of tests is introduced; it includes not only both commonly used versions of Raabe’s test, but also Schl¨omilch’s test.

References

[1] BROMWICH, T. J. I’A.: An Introduction to the Theory of Infinite Series (3rd ed.), Chelsea, New York, NY, 1991.
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[2] FICHTENHOLZ, G. M.: Differential- und Integralrechnung, 14. Aufgabe, H. Deutsch, Frankfurt am Main, 1999.
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[3] KNOPP, K.: Theory and Application of Infinite Series (2nd. ed.), Blackie & Son, Ltd., London, 1964.
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[4] PRUS-WI´SNIOWSKI, F.: A refinement of Raabe’s test, Amer. Math. Monthly 115 (2008), 249-252.10.1080/00029890.2008.11920522
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[5] VOROBEV, N. N.: Teoria Riadov, Nauka, Moskva, 1975. (In Russian)
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Articles in this issue

DOI: https://doi.org/10.2478/v10127-009-0012-y | Journal eISSN: 1338-9750 | Journal ISSN: 12103195

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Language: English

Page range: 119 - 130

Published on: Nov 12, 2012

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

series,

tests for convergence.

Related subjects:

Mathematics,

General mathematics

© 2012 Franciszek Prus-Wiśniowski, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons License.

Volume 42 (2009): Issue 1 (April 2009)