DLMF:16.2.E4

MaRDI QIDQ5883

• Label: DLMF:16.2.E4

Digital Library of Mathematical Functions ID 16.2.E4

${\displaystyle{\displaystyle\sum_{k=0}^{m}\frac{{\left(\mathbf{a}\right)_{k}}}{{\left(\mathbf{b}\right)_{k}}}\frac{z^{k}}{k!}=\frac{{\left(\mathbf{a}\right)_{m}}z^{m}}{{\left(\mathbf{b}\right)_{m}}m!}{{}_{q+2}F_{p}}\left({-m,1,1-m-\mathbf{b}\atop 1-m-\mathbf{a}};\frac{(-1)^{p+q+1}}{z}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}$: alternatively F q p ( a ; b ; z ) or F q p ( a b ; z ) generalized hypergeometric function
• ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$:
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle p}}$: nonnegative integer
• ${\displaystyle{\displaystyle q}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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