Non-terminating Whippleの変換公式の片方の4F3がDixonの和公式で総和できる場合について

$$\newcommand{adari}[0]{\mathrm{adari}} \newcommand{adari}[0]{\mathrm{adari}} \newcommand{adgari}[0]{\mathrm{adgari}} \newcommand{al}[0]{\mathrm{al}} \newcommand{amit}[0]{\mathrm{amit}} \newcommand{anit}[0]{\boldsymbol{anit}} \newcommand{anit}[0]{\mathrm{anit}} \newcommand{answamu}[0]{\mathrm{answamu}} \newcommand{anti}[0]{\mathrm{anti}} \newcommand{ari}[0]{\mathrm{ari}} \newcommand{ARI}[0]{\mathrm{ARI}} \newcommand{ARI}[0]{\mathrm{ARI}} \newcommand{arit}[0]{\mathrm{arit}} \newcommand{as}[0]{\mathrm{as}} \newcommand{axi}[0]{\mathrm{axi}} \newcommand{axit}[0]{\mathrm{axit}} \newcommand{ba}[0]{\boldsymbol{a}} \newcommand{bb}[0]{\boldsymbol{b}} \newcommand{bc}[0]{\boldsymbol{c}} \newcommand{bd}[0]{\boldsymbol{d}} \newcommand{be}[0]{\boldsymbol{e}} \newcommand{bk}[0]{\boldsymbol{k}} \newcommand{bl}[0]{\boldsymbol{l}} \newcommand{BQ}[5]{{}_{#1}\psi_{#2}\left[\begin{matrix}#3\\#4\end{matrix};#5\right]} \newcommand{bw}[0]{\boldsymbol{w}} \newcommand{bx}[0]{\boldsymbol{x}} \newcommand{by}[0]{\boldsymbol{y}} \newcommand{calA}[0]{\mathcal{A}} \newcommand{calS}[0]{\mathcal{S}} \newcommand{CC}[0]{\mathbb{C}} \newcommand{crash}[0]{\mathrm{crash}} \newcommand{der}[0]{\mathrm{der}} \newcommand{DIFF}[0]{\mathrm{DIFF}} \newcommand{EE}[0]{\mathfrak{E}} \newcommand{Eneg}[0]{\mathfrak{E}\text{-}\mathrm{neg}} \newcommand{Enegpush}[0]{\mathfrak{E}\text{-}\mathrm{negpush}} \newcommand{Epush}[0]{\mathfrak{E}\text{-}\mathrm{push}} \newcommand{es}[0]{\mathfrak{es}} \newcommand{Esena}[0]{\mathfrak{E}\text{-}\mathrm{sena}} \newcommand{ess}[0]{\mathfrak{ess}} \newcommand{Eswap}[0]{\mathfrak{E}\text{-}\swap} \newcommand{Eter}[0]{\mathfrak{E}\text{-}\mathrm{ter}} \newcommand{expari}[0]{\mathrm{expari}} \newcommand{ez}[0]{\mathfrak{ez}} \newcommand{F}[5]{{}_{#1}F_{#2}\left[\begin{matrix}#3\\#4\end{matrix};#5\right]} \newcommand{fragari}[0]{\mathrm{fragari}} \newcommand{fragira}[0]{\mathrm{fragira}} \newcommand{gami}[0]{\mathrm{gami}} \newcommand{gamit}[0]{\mathrm{gamit}} \newcommand{gani}[0]{\mathrm{gani}} \newcommand{ganit}[0]{\mathrm{ganit}} \newcommand{gantar}[0]{\mathrm{gantar}} \newcommand{gari}[0]{\mathrm{gari}} \newcommand{GARI}[0]{\mathrm{GARI}} \newcommand{GARI}[0]{\mathrm{GARI}} \newcommand{garit}[0]{\mathrm{garit}} \newcommand{gaxi}[0]{\mathrm{gaxi}} \newcommand{gaxit}[0]{\mathrm{gaxit}} \newcommand{gepar}[0]{\mathrm{gepar}} \newcommand{GIFF}[0]{\mathrm{GIFF}} \newcommand{gira}[0]{\mathrm{gira}} \newcommand{girat}[0]{\mathrm{girat}} \newcommand{gush}[0]{\mathrm{gush}} \newcommand{H}[5]{{}_{#1}H_{#2}\left[\begin{matrix}#3\\#4\end{matrix};#5\right]} \newcommand{He}[0]{\mathfrak{He}} \newcommand{inv}[0]{\mathrm{inv}} \newcommand{invgami}[0]{\mathrm{invgami}} \newcommand{invgani}[0]{\mathrm{invgani}} \newcommand{invgari}[0]{\mathrm{invgari}} \newcommand{invgaxi}[0]{\mathrm{invgaxi}} \newcommand{invgira}[0]{\mathrm{invgira}} \newcommand{invmu}[0]{\mathrm{invmu}} \newcommand{ira}[0]{\mathrm{ira}} \newcommand{irat}[0]{\mathrm{irat}} \newcommand{iwat}[0]{\mathrm{iwat}} \newcommand{lu}[0]{\mathrm{lu}} \newcommand{LU}[0]{\mathrm{LU}} \newcommand{maj}[0]{\mathrm{maj}} \newcommand{mantar}[0]{\mathrm{mantar}} \newcommand{MU}[0]{\mathrm{MU}} \newcommand{neg}[0]{\mathrm{neg}} \newcommand{ol}[0]{\overline} \newcommand{Omantar}[0]{\mathfrak{O}\text{-}\mathrm{mantar}} \newcommand{OO}[0]{\mathfrak{O}} \newcommand{os}[0]{\mathfrak{os}} \newcommand{oss}[0]{\mathfrak{oss}} \newcommand{oz}[0]{\mathfrak{oz}} \newcommand{pari}[0]{\mathrm{pari}} \newcommand{preari}[0]{\mathrm{preari}} \newcommand{preira}[0]{\mathrm{preira}} \newcommand{pus}[0]{\mathrm{pus}} \newcommand{push}[0]{\mathrm{push}} \newcommand{pusnu}[0]{\mathrm{pusnu}} \newcommand{Q}[5]{{}_{#1}\phi_{#2}\left[\begin{matrix}#3\\#4\end{matrix};#5\right]} \newcommand{QQ}[0]{\mathbb{Q}} \newcommand{ras}[0]{\mathrm{ras}} \newcommand{rash}[0]{\mathrm{rash}} \newcommand{re}[0]{\mathfrak{re}} \newcommand{ro}[0]{\mathfrak{r\ddot{o}}} \newcommand{Se}[0]{\mathfrak{Se}} \newcommand{sh}[0]{\,\text{ш}\,} \newcommand{So}[0]{\mathfrak{S\ddot{o}}} \newcommand{swamu}[0]{\mathrm{swamu}} \newcommand{swap}[0]{\mathrm{swap}} \newcommand{To}[0]{\mathfrak{T\ddot{o}}} \newcommand{ZZ}[0]{\mathbb{Z}} $$