Mathematics > Classical Analysis and ODEs
[Submitted on 6 May 2024
]
Title: On the generalized Dirichlet beta and Riemann zeta functions and Ramanujan-type formulae for beta and zeta values
Title: 关于广义的狄利克雷贝塔函数和黎曼ζ函数以及拉马努金型公式用于贝塔和ζ值
Abstract: We define the generalized Dirichlet beta and Riemann zeta functions in terms of the integrals, involving powers of the hyperbolic secant and cosecant functions. The corresponding functional equations are established. Some consequences of the Ramanujan identity for zeta values at odd integers are investigated and new formulae of the Ramanujan type are obtained.
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