Abstract
Formulas are given for the fast expansion of a smooth function on a segment, which allows one to increase the rate of convergence of the Fourier series unlimitedly depending on the order of expansion. The theorems on the convergence of a series in fast expansion, the possibility of its multiple termwise differentiation, the uniqueness of fast expansion, are proved, and the error in the residual series in fast expansion is estimated. Algorithms for applying fast expansion are given, the concept of the fast expansion operator, which is necessary for solving nonlinear integro-differential problems, is introduced.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
