Riemann Integral of Functions R into C

Pole DC	Wartość	Język
dc.contributor.author	Miyajima, Keiichi	-
dc.contributor.author	Kato, Takahiro	-
dc.contributor.author	Shidama, Yasunari	-
dc.date.accessioned	2015-12-02T18:02:53Z	-
dc.date.available	2015-12-02T18:02:53Z	-
dc.date.issued	2010	-
dc.identifier.citation	Formalized Mathematics, Volume 18, Issue 4, 2010, Pages 201-206	-
dc.identifier.issn	1426-2630	-
dc.identifier.issn	1898-9934	-
dc.identifier.uri	http://hdl.handle.net/11320/3576	-
dc.description.abstract	In this article, we define the Riemann Integral on functions R into C and proof the linearity of this operator. Especially, the Riemann integral of complex functions is constituted by the redefinition about the Riemann sum of complex numbers. Our method refers to the [19].	-
dc.language.iso	en	-
dc.publisher	De Gruyter Open	-
dc.title	Riemann Integral of Functions R into C	-
dc.type	Article	-
dc.identifier.doi	10.2478/v10037-010-0024-8	-
dc.description.Affiliation	Miyajima Keiichi - Faculty of Engineering, Ibaraki University, Hitachi, Japan	-
dc.description.Affiliation	Kato Takahiro - Faculty of Engineering, Graduate School of Ibaraki University, Hitachi, Japan	-
dc.description.Affiliation	Shidama Yasunari - Shinshu University, Nagano, Japan	-
dc.description.references	Agnieszka Banachowicz and Anna Winnicka. Complex sequences. Formalized Mathematics, 4(1):121-124, 1993.	-
dc.description.references	Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.	-
dc.description.references	Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.	-
dc.description.references	Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.	-
dc.description.references	Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.	-
dc.description.references	Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.	-
dc.description.references	Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.	-
dc.description.references	Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.	-
dc.description.references	Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.	-
dc.description.references	Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93-102, 1999.	-
dc.description.references	Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Darboux's theorem. Formalized Mathematics, 9(1):197-200, 2001.	-
dc.description.references	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.	-
dc.description.references	Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Scalar multiple of Riemann definite integral. Formalized Mathematics, 9(1):191-196, 2001.	-
dc.description.references	Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.	-
dc.description.references	Keiichi Miyajima and Yasunari Shidama. Riemann integral of functions from R into Rn. Formalized Mathematics, 17(2):179-185, 2009, doi: 10.2478/v10037-009-0021-y.	-
dc.description.references	Adam Naumowicz. Conjugate sequences, bounded complex sequences and convergent complex sequences. Formalized Mathematics, 6(2):265-268, 1997.	-
dc.description.references	Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.	-
dc.description.references	Yasunari Shidama and Artur Korniłowicz. Convergence and the limit of complex sequences. Series. Formalized Mathematics, 6(3):403-410, 1997.	-
dc.description.references	Murray R. Spiegel. Theory and Problems of Vector Analysis. McGraw-Hill, 1974.	-
dc.description.references	Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.	-
dc.description.references	Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.	-
Występuje w kolekcji(ach):	Formalized Mathematics, 2010, Volume 18, Issue 4

Pliki w tej pozycji:

Plik	Opis	Rozmiar	Format
v10037-010-0024-8.pdf		251,96 kB	Adobe PDF	Otwórz

Pokaż uproszczony widok rekordu Zobacz statystyki

Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL