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The Sum and Product of Finite Sequences of Complex Numbers Cover

The Sum and Product of Finite Sequences of Complex Numbers

Formalized Mathematics
Volume 18 (2010): Issue 2 (June 2010)
By: Keiichi Miyajima and  Takahiro Kato  
Open Access
|Jan 2011

References

  1. [1] Kanchun and Yatsuka Nakamura. The inner product of finite sequences and of points of n-dimensional topological space. Formalized Mathematics, 11(2):179-183, 2003.
    Search in Google Scholar
  2. [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
    Search in Google Scholar
  3. [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
    Search in Google Scholar
  4. [4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
    Search in Google Scholar
  5. [5] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
    Search in Google Scholar
  6. [6] Czesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643-649, 1990.
    Search in Google Scholar
  7. [7] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
    Search in Google Scholar
  8. [8] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
    Search in Google Scholar
  9. [9] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
    Search in Google Scholar
  10. [10] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
    Search in Google Scholar
  11. [11] Keith E. Hirst. Numbers, Sequences and Series. Butterworth-Heinemann, 1984.
    Search in Google Scholar
  12. [12] Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477-481, 1990.
    Search in Google Scholar
  13. [13] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
    Search in Google Scholar
  14. [14] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.
    Search in Google Scholar
  15. [15] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
    Search in Google Scholar
DOI: https://doi.org/10.2478/v10037-010-0014-x | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
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Language: English
Page range: 107 - 111
Published on: Jan 5, 2011
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Related subjects:
Mathematics,
General mathematics,
Computer sciences,
Computer sciences, other

© 2011 Keiichi Miyajima, Takahiro Kato, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 18 (2010): Issue 2 (June 2010)