\left({\textstyle\ifrac{\prod\limits_{{k=1}}^{{q+1}}\mathop{\Gamma\/}\nolimits% \!\left(a_{k}\right)}{\prod\limits_{{k=1}}^{q}\mathop{\Gamma\/}\nolimits\!% \left(b_{k}\right)}}\right)\mathop{{{}_{{q+1}}F_{{q}}}\/}\nolimits\!\left({a_{% 1},\dots,a_{{q+1}}\atop b_{1},\dots,b_{q}};z\right)=\sum_{{j=1}}^{{q+1}}\left(% z_{0}-z\right)^{{-a_{j}}}\sum_{{n=0}}^{\infty}\frac{\mathop{\Gamma\/}\nolimits% \!\left(a_{j}+n\right)}{n!}\*\left({\textstyle\ifrac{\prod\limits_{{\substack{% k=1\\ k\neq j}}}^{{q+1}}\mathop{\Gamma\/}\nolimits\!\left(a_{k}-a_{j}-n\right)}{% \prod\limits_{{k=1}}^{q}\mathop{\Gamma\/}\nolimits\!\left(b_{k}-a_{j}-n\right)% }}\right)\*\mathop{{{}_{{q+1}}F_{{q}}}\/}\nolimits\!\left({a_{1}-a_{j}-n,\dots% ,a_{{q+1}}-a_{j}-n\atop b_{1}-a_{j}-n,\dots,b_{q}-a_{j}-n};z_{0}\right)\left(z% -z_{0}\right)^{{-n}}.
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