Cauchy’s Integral Formula for Derivatives

Ravi P. Agarwal (), Kanishka Perera () and Sandra Pinelas ()
Additional contact information
Ravi P. Agarwal: Florida Institute of Technology, Department of Mathematics
Kanishka Perera: Florida Institute of Technology, Department of Mathematical Sciences
Sandra Pinelas: Azores University, Department of Mathematics

Chapter Lecture 18 in An Introduction to Complex Analysis, 2011, pp 116-124 from Springer

Abstract: Abstract In this lecture, we shall show that, for an analytic function in a given domain, all the derivatives exist and are analytic. This result leads to Cauchy’s integral formula for derivatives. Next, we shall prove Morera’s Theorem, which is a converse of the Cauchy–Goursat Theorem. We shall also establish Cauchy’s inequality for the derivatives, which plays an important role in proving Liouville’s Theorem.

Date: 2011
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-0195-7_18

Ordering information: This item can be ordered from
http://www.springer.com/9781461401957

DOI: 10.1007/978-1-4614-0195-7_18

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().