Mr. Chuyu Hu Profile

Chuyu Hu

at Guangxi University for Nationalities

SPIE Involvement:

Author

Publications (1)

This will count as one of your downloads.

You will have access to both the presentation and article (if available).

DOWNLOAD NOW

This content is available for download via your institution's subscription. To access this item, please sign in to your personal account.

Email or Username Forgot your username?

Password Forgot your password?

Show

Keep me signed in

No SPIE account? Create an account

Proceedings Article | 27 September 2022 Paper

Applications of the infinite series of Cauchy residue theorem and its extensions

Yanjun Chen, Chuyu Hu, Shuxian Song

Proceedings Volume 12345, 1234507 (2022) https://doi.org/10.1117/12.2648816

KEYWORDS: Mathematics, Calculus, Algorithms

Read Abstract +

In this paper, the general concept of residue and general residue formulas are introduced. The general residue provides a method to study functions with infinite isolated singularities and the non-isolated singularities, which are the limits of sequences of isolated singularities. The general concept and residue theorem cover the shortage of the classical Cauchy residue theorem which can only deal with finite many isolated singularities. Then one uses the extended residue theorem on non-isolated singularities to calculate some infinite series. One can compute some classical series coming from different branches of mathematics, such as elliptic functions, number theory, and other examples. Using this method, one can see that it is a very useful method to deal with absolutely convergent series. More excitingly, this way is easy to use unlike most other methods for series. Thus, one can image that it has amazing applications in complex analysis and even other branches.

My Library

You currently do not have any folders to save your paper to! Create a new folder below.

Folder Name

Folder Description

View contact details

UPDATE YOUR PROFILE

Is this your profile? Update it now.

Sign into your SPIE.org account

Don’t have a profile and want one?

Create an account on SPIE.org

Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks. You are receiving this notice because your organization may not have SPIE eBooks access.*

*Shibboleth/Open Athens users─please sign in to access your institution's subscriptions.

To obtain this item, you may purchase the complete book in print or electronic format on SPIE.org.

ORGANIZATIONAL
Sign in with credentials provided by your organization.

Organizational Username

Organizational Password

Show/Hide Password

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members:

Non-members: ADD TO CART

Keywords/Phrases

Search In:

Publication Years