VALUES OF THE RIEMANN ZETA-FUNCTION AND INTEGRALS INVOLVING LOG (2 SINH THETA 2) AND LOG (2 SIN THETA/2)/

Authors
ZHANG NY WILLIAMS KS
Citation
Ny. Zhang et Ks. Williams, VALUES OF THE RIEMANN ZETA-FUNCTION AND INTEGRALS INVOLVING LOG (2 SINH THETA 2) AND LOG (2 SIN THETA/2)/, Pacific journal of mathematics, 168(2), 1995, pp. 271-289
Citations number
9
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Pacific journal of mathematics → ACNP
ISSN journal
00308730
Volume
168
Issue
2
Year of publication
1995
Pages
271 - 289
Database
ISI
SICI code
0030-8730(1995)168:2<271:VOTRZA>2.0.ZU;2-L
Abstract
Integrals involving the functions log (2 sinh(theta/2)) and log (2 sin (theta/2)) are studied, particularly their relationship to the values of the Riemann zeta function at integral arguments. For example genera l formulae are proved which contain the known results integral(0)(pi/3 ) log(2) (2 sin(theta/2)) d theta = 7 pi(3)/108, integral(0)(pi/3) the ta log(2) (2 sin(theta/2)) d theta = 17 pi(4)/6480, integral(0)(pi/3) (log(4)(2 sin(theta/2)) - 3/2 theta(2)(2 sin (theta/2))) d theta = 253 pi(5)/3240, integral 0 pi/3 (theta log(4)(2 sin (theta/2) - theta(3)/ 2 log(2 sin (theta 2))) d theta = 313 pi(6)/408240, as special cases.