ancont - Analytic Continuation See Arfken Weber pp...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Analytic Continuation See Arfken & Weber pp 432-434 (in section 6.5 on Laurent expansions) for some of the material below. Our description here will closely follow [1]. 1 Definition The intersection of two domains (regions in the complex plane) D 1 , D 2 , denoted D 1 D 2 , is the set of all points common to both D 1 and D 2 . The union of two domains D 1 , D 2 , denoted D 1 D 2 , is the set of all points in either D 1 or D 2 . Now, suppose you have two domains D 1 and D 2 , such that the intersection is nonempty and connected, and a function f 1 that is analytic over the domain D 1 . If there exists a function f 2 that is analytic over the domain D 2 and such that f 1 = f 2 on the intersection D 1 D 2 , then we say f 2 is an analytic continuation of f 1 into domain D 2 . Now, whenever an analytic continuation exists, it is unique. The reason for this is a basic mathematical result from the theory of complex variables: A function that is analytic in a domain D is uniquely determined over D by its values over a domain, or along an arc, interior to D .
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern