DLMF:16.13.E2 (Q5250)

From DRMF
Revision as of 14:40, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:16.13.E2
No description defined

    Statements

    Defining formula
    F 2 ⁡ ( α ; β , β ′ ; γ , γ ′ ; x , y ) = ∑ m , n = 0 ∞ ( α ) m + n ⁢ ( β ) m ⁢ ( β ′ ) n ( γ ) m ⁢ ( γ ′ ) n ⁢ m ! ⁢ n ! ⁢ x m ⁢ y n , Appell-F-2 𝛼 𝛽 superscript 𝛽 ′ 𝛾 superscript 𝛾 ′ 𝑥 𝑦 superscript subscript 𝑚 𝑛 0 Pochhammer 𝛼 𝑚 𝑛 Pochhammer 𝛽 𝑚 Pochhammer superscript 𝛽 ′ 𝑛 Pochhammer 𝛾 𝑚 Pochhammer superscript 𝛾 ′ 𝑛 𝑚 𝑛 superscript 𝑥 𝑚 superscript 𝑦 𝑛 {\displaystyle{\displaystyle{F_{2}}\left(\alpha;\beta,\beta^{\prime};\gamma,% \gamma^{\prime};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}}{\left(\gamma^{\prime}\right)_{n}}m!n!}x^{m}y^{n},}}
    0 references
    DLMF id
    DLMF:16.13.E2
    0 references
    constraint
    | x | + | y | < 1 𝑥 𝑦 1 {\displaystyle{\displaystyle|x|+|y|<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.m1aadec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5250&oldid=49680"