DLMF:16.13.E1 (Q5249): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
Defining formula:

( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
 
xml-id: C5.S2.SS3.m1adec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5adec

Latest revision as of 14:40, 2 January 2020

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DLMF:16.13.E1
No description defined

    Statements

    Defining formula
    F 1 ⁡ ( α ; β , β ′ ; γ ; x , y ) = ∑ m , n = 0 ∞ ( α ) m + n ⁢ ( β ) m ⁢ ( β ′ ) n ( γ ) m + n ⁢ m ! ⁢ n ! ⁢ x m ⁢ y n , Appell-F-1 𝛼 𝛽 superscript 𝛽 ′ 𝛾 𝑥 𝑦 superscript subscript 𝑚 𝑛 0 Pochhammer 𝛼 𝑚 𝑛 Pochhammer 𝛽 𝑚 Pochhammer superscript 𝛽 ′ 𝑛 Pochhammer 𝛾 𝑚 𝑛 𝑚 𝑛 superscript 𝑥 𝑚 superscript 𝑦 𝑛 {\displaystyle{\displaystyle{F_{1}}\left(\alpha;\beta,\beta^{\prime};\gamma;x,% y\right)=\sum_{m,n=0}^{\infty}\frac{{\left(\alpha\right)_{m+n}}{\left(\beta% \right)_{m}}{\left(\beta^{\prime}\right)_{n}}}{{\left(\gamma\right)_{m+n}}m!n!% }x^{m}y^{n},}}
    0 references
    DLMF id
    DLMF:16.13.E1
    0 references
    constraint
    max ⁡ ( | x | , | y | ) < 1 𝑥 𝑦 1 {\displaystyle{\displaystyle\max\left(|x|,|y|\right)<1}}
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
     
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