Complex Function Differentiability
Chanapat Pacharapokin ; Hiroshi Yamazaki ; Yasunari Shidama ; Yatsuka Nakamura
Formalized Mathematics, Tome 17 (2009), p. 67-72 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:266915 
@article{bwmeta1.element.doi-10_2478_v10037-009-0007-9,
     author = {Chanapat Pacharapokin and Hiroshi Yamazaki and Yasunari Shidama and Yatsuka Nakamura},
     title = {Complex Function Differentiability},
     journal = {Formalized Mathematics},
     volume = {17},
     year = {2009},
     pages = {67-72},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-009-0007-9}
}

Chanapat Pacharapokin; Hiroshi Yamazaki; Yasunari Shidama; Yatsuka Nakamura. Complex Function Differentiability. Formalized Mathematics, Tome 17 (2009) pp. 67-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-009-0007-9/

[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. | Zbl 06213858

[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. | Zbl 0951.93523

[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.