Four explicit continued fractions for values of the Lerch transcendent and the Hurwitz zeta function

Andrius Grigutis, Yuri Matiyasevich, Lukas Turčinskas

We prove four explicit continued fraction representations for the Lerch transcendent $\Phi (z,s,M+1)$, where $\Re M>0$ and $(z,s)\in \{(-1,1),(-1,2),(1,2),(1,3)\}$. All of the continu…