The Sum and Product of Finite Sequences of Complex Numbers

Keiichi Miyajima; Takahiro Kato

Formalized Mathematics (2010)

  • Volume: 18, Issue: 2, page 107-111
  • ISSN: 1426-2630

Abstract

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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].

How to cite

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Keiichi Miyajima, and Takahiro Kato. "The Sum and Product of Finite Sequences of Complex Numbers." Formalized Mathematics 18.2 (2010): 107-111. <http://eudml.org/doc/266873>.

@article{KeiichiMiyajima2010,
abstract = {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].},
author = {Keiichi Miyajima, Takahiro Kato},
journal = {Formalized Mathematics},
language = {eng},
number = {2},
pages = {107-111},
title = {The Sum and Product of Finite Sequences of Complex Numbers},
url = {http://eudml.org/doc/266873},
volume = {18},
year = {2010},
}

TY - JOUR
AU - Keiichi Miyajima
AU - Takahiro Kato
TI - The Sum and Product of Finite Sequences of Complex Numbers
JO - Formalized Mathematics
PY - 2010
VL - 18
IS - 2
SP - 107
EP - 111
AB - 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].
LA - eng
UR - http://eudml.org/doc/266873
ER -

References

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  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. 
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  5. [5] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990. 
  6. [6] Czesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643-649, 1990. 
  7. [7] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990. 
  8. [8] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990. 
  9. [9] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  10. [10] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990. 
  11. [11] Keith E. Hirst. Numbers, Sequences and Series. Butterworth-Heinemann, 1984. 
  12. [12] Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477-481, 1990. 
  13. [13] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990. 
  14. [14] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990. 
  15. [15] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 

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