We prove that a two-variable $p$-adic ${l}_{q}$-function has the series expansion ${l}_{p,q}(s,t,\chi )=\vspace{1pt}{([2]}_{q}/{[2]}_{F}){\sum }_{a=1,(p,a)=1}^{F}{(-1)}^{a}(\chi (a){q}^{a}/{\langle a+pt\rangle }^{s}){\sum }_{m=0}^{\infty }(\begin{smallmatrix}-s\\ \vspace{0pt}m\end{smallmatrix}){(F/\langle a+pt\rangle )}^{m}{E}_{m,{q}^{F}}^{\ast}$ which interpolates the values ${l}_{p,q}(-n,t,\chi )={E}_{n,{\chi }_{n},q}^{\ast}(pt)-{p}^{n}{\chi }_{n}(p)({[2]}_{q}/{[2]}_{{q}^{p}}){E}_{n,{\chi }_{n},{q}^{p}}^{\ast}(t)$, whenever $n$ is a nonpositive integer. The proof of this original construction is
due to Kubota and Leopoldt in 1964, although the method given in this note
is due to Washington.
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