New integral representations are obtained for multiple Apéry-like series, expressed via polylogarithms, Legendre chi functions and inverse tangent integrals, together with a new identity as linear combinations of Dirichlet eta products.
Lewin,Polylogarithms and Associated Functions, North Holland, New York
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Integral Representations for Multiple Ap\'ery-Like Series
New integral representations are obtained for multiple Apéry-like series, expressed via polylogarithms, Legendre chi functions and inverse tangent integrals, together with a new identity as linear combinations of Dirichlet eta products.