Complex Integral
Masahiko Yamazaki; Hiroshi Yamazaki; Yasunari Shidama; Katsumi Wasaki
Formalized Mathematics (2009)
- Volume: 17, Issue: 4, page 233-236
- ISSN: 1426-2630
Access Full Article
topAbstract
topHow to cite
topMasahiko Yamazaki, et al. "Complex Integral." Formalized Mathematics 17.4 (2009): 233-236. <http://eudml.org/doc/267228>.
@article{MasahikoYamazaki2009,
abstract = {In this article, we defined complex curve and complex integral. Then we have proved the linearity for the complex integral. Furthermore, we have proved complex integral of complex curve's connection is the sum of each complex integral of individual complex curve.},
author = {Masahiko Yamazaki, Hiroshi Yamazaki, Yasunari Shidama, Katsumi Wasaki},
journal = {Formalized Mathematics},
language = {eng},
number = {4},
pages = {233-236},
title = {Complex Integral},
url = {http://eudml.org/doc/267228},
volume = {17},
year = {2009},
}
TY - JOUR
AU - Masahiko Yamazaki
AU - Hiroshi Yamazaki
AU - Yasunari Shidama
AU - Katsumi Wasaki
TI - Complex Integral
JO - Formalized Mathematics
PY - 2009
VL - 17
IS - 4
SP - 233
EP - 236
AB - In this article, we defined complex curve and complex integral. Then we have proved the linearity for the complex integral. Furthermore, we have proved complex integral of complex curve's connection is the sum of each complex integral of individual complex curve.
LA - eng
UR - http://eudml.org/doc/267228
ER -
References
top- [1] Czesław Byliński. Basic functions and operations on functions. Formalized Mathematics, 1(1):245-254, 1990.
- [2] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
- [3] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
- [4] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
- [5] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
- [6] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
- [7] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. Formalized Mathematics, 9(2):281-284, 2001.
- [8] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
- [9] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.
- [10] Takashi Mitsuishi, Katsumi Wasaki, and Yasunari Shidama. Property of complex functions. Formalized Mathematics, 9(1):179-184, 2001. Zbl0951.93523
- [11] Konrad Raczkowski and Paweł Sadowski. Real function continuity. Formalized Mathematics, 1(4):787-791, 1990.
- [12] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.
- [13] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
- [14] Yasunari Shidama and Artur Korniłowicz. Convergence and the limit of complex sequences. Series. Formalized Mathematics, 6(3):403-410, 1997.
- [15] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.
- [16] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
- [17] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.