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Formalized Mathematics

(a computer assisted approach)

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Volume 17, Issue 2 (Jan 2009)

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Complex Function Differentiability

Chanapat Pacharapokin
  • Shinshu University, Nagano, Japan
/ Hiroshi Yamazaki
  • Shinshu University, Nagano, Japan
/ Yasunari Shidama
  • Shinshu University, Nagano, Japan
/ Yatsuka Nakamura
  • Shinshu University, Nagano, Japan
Published Online: 2009-07-14 | DOI: https://doi.org/10.2478/v10037-009-0007-9

Complex Function Differentiability

For a complex valued function defined on its domain in complex numbers the differentiability in a single point and on a subset of the domain is presented. The main elements of differential calculus are developed. The algebraic properties of differential complex functions are shown.

  • [1] Agnieszka Banachowicz and Anna Winnicka. Complex sequences. Formalized Mathematics, 4(1):121-124, 1993.

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

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

  • [6] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.

  • [7] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

  • [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] Jarosław Kotowicz. Monotone real sequences. Subsequences. Formalized Mathematics, 1(3):471-475, 1990.

  • [11] Jarosław Kotowicz. Partial functions from a domain to a domain. Formalized Mathematics, 1(4):697-702, 1990.

  • [12] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.

  • [13] Takashi Mitsuishi, Katsumi Wasaki, and Yasunari Shidama. Property of complex sequence and continuity of complex function. Formalized Mathematics, 9(1):185-190, 2001.

  • [14] Adam Naumowicz. Conjugate sequences, bounded complex sequences and convergent complex sequences. Formalized Mathematics, 6(2):265-268, 1997.

  • [15] Yasunari Shidama and Artur Korniłowicz. Convergence and the limit of complex sequences. Series. Formalized Mathematics, 6(3):403-410, 1997.

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

  • [17] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

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

  • [19] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

About the article


Published Online: 2009-07-14

Published in Print: 2009-01-01



Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-009-0007-9. Export Citation

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[1]
Katuhiko Kanazashi, Hiroyuki Okazaki, and Yasunari Shidama
Formalized Mathematics, 2012, Volume 20, Number 1
[2]
Hiroshi Yamazaki, Yasunari Shidama, Yatsuka Nakamura, and Chanapat Pacharapokin
Formalized Mathematics, 2009, Volume 17, Number 2

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