TY - JOUR
T1 - The remainder term in fourier series and its relationship with the basel problem
AU - Barrera-Figueroa, V.
AU - Lucas-Bravo, A.
AU - López-Bonilla, J.
N1 - Publisher Copyright:
© 2007, Eszterhazy Karoly College. All rights reserved.
PY - 2007
Y1 - 2007
N2 - In this paper it is shown several approximation formulae for the remainder term of the Fourier series for a wide class of functions satisfying specific boundary conditions. Also it is shown that the remainder term is related with the Basel problem and the Riemann zeta function, which can be interpreted as the energy of discrete-time signals; from this point of view, their energy can be calculated with a direct formula instead of an infinite series. The validity of this algorithm is established by means several proofs.
AB - In this paper it is shown several approximation formulae for the remainder term of the Fourier series for a wide class of functions satisfying specific boundary conditions. Also it is shown that the remainder term is related with the Basel problem and the Riemann zeta function, which can be interpreted as the energy of discrete-time signals; from this point of view, their energy can be calculated with a direct formula instead of an infinite series. The validity of this algorithm is established by means several proofs.
KW - Basel problem
KW - Discrete-time signal
KW - Fourier series remainder term
KW - Slow varying-type series
UR - http://www.scopus.com/inward/record.url?scp=85037086305&partnerID=8YFLogxK
M3 - Artículo
SN - 1787-5021
VL - 34
SP - 17
EP - 28
JO - Annales Mathematicae et Informaticae
JF - Annales Mathematicae et Informaticae
ER -