DLMF:16.3.E3 (Q5190): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11694 / rank
 
Normal rank
Property / Symbols used: Q11694 / qualifier
 
Defining formula:

b , b 1 , … , b q 𝑏 subscript 𝑏 1 … subscript 𝑏 𝑞 {\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}

b,b_{1},\ldots,b_{q}
Property / Symbols used: Q11694 / qualifier
 
xml-id: C16.S1.XMD5.m1bdec

Latest revision as of 14:29, 2 January 2020

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DLMF:16.3.E3
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    Statements

    Defining formula
    ( z ⁢ d d z ⁡ z ) n ⁢ ( z γ - 1 ⁢ F q p + 1 ⁡ ( γ , a 1 , … , a p b 1 , … , b q ; z ) ) = ( γ ) n ⁢ z γ + n - 1 ⁢ F q p + 1 ⁡ ( γ + n , a 1 , … , a p b 1 , … , b q ; z ) , superscript 𝑧 derivative 𝑧 𝑧 𝑛 superscript 𝑧 𝛾 1 Gauss-hypergeometric-pFq 𝑝 1 𝑞 𝛾 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 Pochhammer 𝛾 𝑛 superscript 𝑧 𝛾 𝑛 1 Gauss-hypergeometric-pFq 𝑝 1 𝑞 𝛾 𝑛 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}% \left(z^{\gamma-1}{{}_{p+1}F_{q}}\left({\gamma,a_{1},\dots,a_{p}\atop b_{1},% \dots,b_{q}};z\right)\right)={\left(\gamma\right)_{n}}z^{\gamma+n-1}{{}_{p+1}F% _{q}}\left({\gamma+n,a_{1},\dots,a_{p}\atop b_{1},\dots,b_{q}};z\right),}}
    0 references
    DLMF id
    DLMF:16.3.E3
    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.m1abdec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1abdec
    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.m2abdec
    0 references
    Q11690
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C16.S1.XMD1.m1bdec
    0 references
    Q11691
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C16.S1.XMD2.m1bdec
    0 references
    Q11692
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C16.S1.XMD3.m1bdec
    0 references
    Q11693
    Defining formula
    a , a 1 , … , a p 𝑎 subscript 𝑎 1 … subscript 𝑎 𝑝 {\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}
    xml-id
    C16.S1.XMD4.m1bdec
    0 references
    Q11694
    Defining formula
    b , b 1 , … , b q 𝑏 subscript 𝑏 1 … subscript 𝑏 𝑞 {\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}
    xml-id
    C16.S1.XMD5.m1bdec
    0 references
     
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