DLMF:19.28.E4 (Q6612)

From DRMF
Revision as of 14:17, 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:19.28.E4
No description defined

    Statements

    Defining formula
    ∫ 0 1 t σ - 1 ⁢ ( 1 - t ) c - 1 ⁢ R - a ⁡ ( b 1 , b 2 ; t , 1 ) ⁢ d t = Γ ⁡ ( c ) ⁢ Γ ⁡ ( σ ) ⁢ Γ ⁡ ( σ + b 2 - a ) Γ ⁡ ( σ + c - a ) ⁢ Γ ⁡ ( σ + b 2 ) , superscript subscript 0 1 superscript 𝑡 𝜎 1 superscript 1 𝑡 𝑐 1 Carlson-integral-R 𝑎 subscript 𝑏 1 subscript 𝑏 2 𝑡 1 𝑡 Euler-Gamma 𝑐 Euler-Gamma 𝜎 Euler-Gamma 𝜎 subscript 𝑏 2 𝑎 Euler-Gamma 𝜎 𝑐 𝑎 Euler-Gamma 𝜎 subscript 𝑏 2 {\displaystyle{\displaystyle\int_{0}^{1}t^{\sigma-1}(1-t)^{c-1}R_{-a}\left(b_{% 1},b_{2};t,1\right)\mathrm{d}t=\frac{\Gamma\left(c\right)\Gamma\left(\sigma% \right)\Gamma\left(\sigma+b_{2}-a\right)}{\Gamma\left(\sigma+c-a\right)\Gamma% \left(\sigma+b_{2}\right)},}}
    0 references
    DLMF id
    DLMF:19.28.E4
    0 references
    constraint
    ℜ ⁡ σ > max ⁡ ( 0 , a - b 2 ) 𝜎 0 𝑎 subscript 𝑏 2 {\displaystyle{\displaystyle\Re\sigma>\max(0,a-b_{2})}}
    0 references
    c = b 1 + b 2 > 0 𝑐 subscript 𝑏 1 subscript 𝑏 2 0 {\displaystyle{\displaystyle c=b_{1}+b_{2}>0}}
    0 references
    ℜ ⁡ σ > max ⁡ ( 0 , a - b 2 ) 𝜎 0 𝑎 subscript 𝑏 2 {\displaystyle{\displaystyle\Re\sigma>\max(0,a-b_{2})}}
    0 references
    Symbols used
    multivariate hypergeometric function
    Defining formula
    R - a ⁡ ( b 1 , … , b n ; z 1 , … , z n ) Carlson-integral-R 𝑎 subscript 𝑏 1 … subscript 𝑏 𝑛 subscript 𝑧 1 … subscript 𝑧 𝑛 {\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}% };\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}
    xml-id
    C19.S16.E9.m2adec
    0 references
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6612&oldid=45514"