A new way to represent functions as series. (English) Zbl 1428.26005
Summary: In this paper we will show a new way to represent functions as infinite series, finding some conditions under which a function is expandable with this method, and showing how it allows us to find the values of many interesting series. At the end, we will prove one of the main results of the paper, a representation theorem.
MSC:
| 26A06 | One-variable calculus |
| 40A30 | Convergence and divergence of series and sequences of functions |
| 41A58 | Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) |
References:
| [1] | Apostol T.M., Calculus, Vol. I: One-variable calculus, with an introduction to linear algebra, Second edition Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London 1967. · Zbl 0148.28201 |
| [2] | Edwards R.E., Fourier Series: A Modern Introduction, Vol. 1, Second edition, Graduate Texts in Mathematics, Springer-Verlag, New York-Berlin, 1979. · Zbl 0424.42001 |
| [3] | Jeffreys H., Swirles B., Methods of Mathematical Physics, Reprint of the third (1956) edition, Cambridge University Press, Cambridge, 1999. · Zbl 0202.27301 |
| [4] | Katznelson Y., An Introduction to Harmonic Analysis, Third edition, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 2004. · Zbl 0169.17902 |
| [5] | Knopp K., Theory and Applications of Infinite Series, Dover Publications, Dover Books on Mathematics, 1990. |
| [6] | Lang S., A First Course in Calculus, Undergraduate Texts in Mathematics, Springer, 5th edition, 1998. |
| [7] | Rudin W., Principles of Mathematical Analysis, Third edition, International Series in Pure and Applied Mathematics, McGraw-Hill Book Co., New York-Auckland-Düsseldorf, 1976. · Zbl 0148.02903 |
| [8] | Rudin W., Real and Complex Analysis, Third edition, McGraw-Hill Book Co., New York, 1987. · Zbl 0925.00005 |
| [9] | Stein E., Shakarchi R., Fourier Analysis: An introduction, Princeton Lectures in Analysis, Princeton University Press, Princeton, NJ, 2003. · Zbl 1026.42001 |
| [10] | Tolstov G.P., Fourier Series, Dover Publications, Dover Books on Mathematics, 1976. · Zbl 0358.42001 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
