Mathematical Analysis of Fourier Expansion Using Gauss Partial Sum

2nd International Scientific Conference (Pure Sciences, Brilliant Creativity and Renewed Building)

Albuamer, Ansam Ghazi Nsaif^1

Department of Mathematics, Faculty of Computer Science and Mathematics, University of Wassit, Iraq^1

关键词: Continuous functions;    Fourier coefficients;    Fourier expansion;    Gauss Partial Sum;    Mathematical analysis;    Periodic function;    Piecewise continuous functions;    Uniformly continuous;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/571/1/012033/pdf
DOI  :  10.1088/1757-899X/571/1/012033

来源: IOP

【 摘 要 】

Fourier series is one of major specific and standard series of periodic functions that can be found in a wide range of theoretical and practical applications. Despite the Fourier series is old but still brand new in their practical applications especially in the field of communications. The present paper is a new version of the mathematical analysis for such a series using the partial Gauss sum. The functions that will be discussed herein are uniformly continuous and periodic. It is important also that by studying extension of the Fourier series sum for periodic functions, this will be helpful for one to be able to extend Gauss partial sum. The theoretical implementation is proved by solving an example and the results seem to be acceptable.