DLMF:16.3.E4 (Q5191)

From DRMF
Revision as of 15:51, 29 December 2019 by Admin (talk | contribs) (‎Created a new Item: Wikidata Toolkit example test item creation)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:16.3.E4
No description defined

    Statements

    d n d z n ( z γ - 1 F q + 1 p ( a 1 , , a p γ , b 1 , , b q ; z ) ) = ( γ - n ) n z γ - n - 1 F q + 1 p ( a 1 , , a p γ - n , b 1 , , b q ; z ) . derivative 𝑧 𝑛 superscript 𝑧 𝛾 1 Gauss-hypergeometric-pFq 𝑝 𝑞 1 subscript 𝑎 1 subscript 𝑎 𝑝 𝛾 subscript 𝑏 1 subscript 𝑏 𝑞 𝑧 Pochhammer 𝛾 𝑛 𝑛 superscript 𝑧 𝛾 𝑛 1 Gauss-hypergeometric-pFq 𝑝 𝑞 1 subscript 𝑎 1 subscript 𝑎 𝑝 𝛾 𝑛 subscript 𝑏 1 subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(z^% {\gamma-1}{{}_{p}F_{q+1}}\left({a_{1},\dots,a_{p}\atop\gamma,b_{1},\dots,b_{q}% };z\right)\right)={\left(\gamma-n\right)_{n}}z^{\gamma-n-1}{{}_{p}F_{q+1}}% \left({a_{1},\dots,a_{p}\atop\gamma-n,b_{1},\dots,b_{q}};z\right).}}
    0 references
    DLMF:16.3.E4
    0 references