Generalized Dirichlet eta functions are expressed as Gamma-process expectations, yielding a Riccati equation whose negative forcing proves strict concavity, log-concavity, positivity and monotonicity of the log-derivative, plus precise large-t asymptotics.
Sondow,Double integrals for Euler’s constant andlog(4/π)and an analog of Hadjicostas’s formula, Amer
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Riccati--Gamma Dynamics for Concavity and Asymptotics of Generalized Dirichlet Eta Functions
Generalized Dirichlet eta functions are expressed as Gamma-process expectations, yielding a Riccati equation whose negative forcing proves strict concavity, log-concavity, positivity and monotonicity of the log-derivative, plus precise large-t asymptotics.