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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

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1898-9934
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Volume 18, Issue 2 (Jan 2010)

Issues

The Sum and Product of Finite Sequences of Complex Numbers

Keiichi Miyajima
  • Faculty of Engineering, Ibaraki University, Hitachi, Japan
/ Takahiro Kato
  • Faculty of Engineering, Graduate School of Ibaraki University, Hitachi, Japan
Published Online: 2011-01-05 | DOI: https://doi.org/10.2478/v10037-010-0014-x

The Sum and Product of Finite Sequences of Complex Numbers

This article extends the [10]. We define the sum and the product of the sequence of complex numbers, and formalize these theorems. Our method refers to the [11].

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  • [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.

  • [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

  • [4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.

  • [5] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.

  • [6] Czesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643-649, 1990.

  • [7] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.

  • [8] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.

  • [9] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.

  • [10] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.

  • [11] Keith E. Hirst. Numbers, Sequences and Series. Butterworth-Heinemann, 1984.

  • [12] Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477-481, 1990.

  • [13] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.

  • [14] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.

  • [15] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.

About the article


Published Online: 2011-01-05

Published in Print: 2010-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-010-0014-x. Export Citation

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