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Grafakos, L. (2004) Classical Fourier Analysis. Graduate Texts in Mathematics (Book 249). 2nd Edition, Springer, New York.

has been cited by the following article:

• TITLE: The Connection between the Basel Problem and a Special Integral

  AUTHORS: Haifeng Xu, Jiuru Zhou

  KEYWORDS: Basel Problem, Zeta Function, Bernoulli Numbers, Bernoulli Polynomials

  JOURNAL NAME: Applied Mathematics, Vol.5 No.16, September 4, 2014

  ABSTRACT: By using Fubini theorem or Tonelli theorem, we find that the zeta function value at 2 is equal to a special integral. Furthermore, we find that this special integral is two times of another special integral. By using this fact we give an easy way to calculate the value of the alternating sum of without using the Fourier expansion. Also, we discuss the relationship between Genocchi numbers and Bernoulli numbers and get some results about Bernoulli polynomials.