The Sum and Product of Finite Sequences of Complex Numbers
Keiichi Miyajima ; Takahiro Kato
Formalized Mathematics, Tome 18 (2010), p. 107-111 / Harvested from The Polish Digital Mathematics Library

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].

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:266873
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     author = {Keiichi Miyajima and Takahiro Kato},
     title = {The Sum and Product of Finite Sequences of Complex Numbers},
     journal = {Formalized Mathematics},
     volume = {18},
     year = {2010},
     pages = {107-111},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0014-x}
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Keiichi Miyajima; Takahiro Kato. The Sum and Product of Finite Sequences of Complex Numbers. Formalized Mathematics, Tome 18 (2010) pp. 107-111. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0014-x/

[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.

[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. | Zbl 06213858

[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.