DLMF:16.3.E4 (Q5191): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11690 / rank
 
Normal rank
Property / Symbols used: Q11690 / qualifier
 
Defining formula:

p 𝑝 {\displaystyle{\displaystyle p}}

p
Property / Symbols used: Q11690 / qualifier
 
xml-id: C16.S1.XMD1.m1cdec

Revision as of 14:29, 2 January 2020

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DLMF:16.3.E4
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    Statements

    Defining formula
    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 id
    DLMF:16.3.E4
    0 references
    Symbols used
    Q11125
    Defining formula
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; z ) Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
    xml-id
    C16.S2.m1acdec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1acdec
    0 references
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2acdec
    0 references
    Q11690
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C16.S1.XMD1.m1cdec
    0 references
     
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