论文信息 - On an intriguing integral and some series related to (4)

On an intriguing integral and some series related to (4)

An intriguing log-cosine integral is fully analyzed and shown to have value a rational multiple of rC(4), C being the Riemann zeta function. From this we deduce by means of generating functions and Parseval's identity the sums of certain series previously established by a completely different method.

Jonathan M. Borwein | David Borwein | J. Borwein | D. Borwein

[1] K. Stromberg. Introduction to classical real analysis , 1981 .

[2] R. B. Burckel,et al. An Introduction to Classical Complex Analysis: Vol. 1 , 1979 .

[3] T. Apostol. Mathematical Analysis , 1957 .

[4] P. J. de Doelder,et al. On some series containing p (x)—p (y)and 9 p (x)—p (y) 2 for certain values of x and y , 1991 .

[5] B. Berndt. Ramanujan’s Notebooks: Part V , 1997 .

[6] Leonard Lewin,et al. Polylogarithms and Associated Functions , 1981 .

[7] Robert B. Burckel,et al. An introduction to classical complex analysis , 1979 .