LOG-TANGENT INTEGRALS AND THE RIEMANN ZETA FUNCTION

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VALUES OF THE RIEMANN ZETA FUNCTION AND INTEGRALS INVOLVING log ( 2 sinhf ) AND

Integrals involving the functions log (2 sinh(0/2)) and log(2sin(0/2)) are studied, particularly their relationship to the values of the Riemann zeta function at integral arguments. For example general formulae are proved which contain the known results Γ log 2 (2sin(0/2))d0 = 7π 3 /108, Jo Γ 01og 2 (2sin(0/2))d0 = 17τr 4 /6480, Jo / (log 4 (2sin(0/2))-^0 2 log 2 (2sin(0/2)))d0 = 253π 5 /3240, ...

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ژورنال

عنوان ژورنال: Mathematical Modelling and Analysis

سال: 2019

ISSN: 1392-6292,1648-3510

DOI: 10.3846/mma.2019.025