DLMF:11.10.E10 (Q4027)

From DRMF
Revision as of 14:55, 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:11.10.E10
No description defined

    Statements

    Defining formula
    S 1 ⁢ ( ν , z ) = ∑ k = 0 ∞ ( - 1 ) k ⁢ ( 1 2 ⁢ z ) 2 ⁢ k Γ ⁡ ( k + 1 2 ⁢ ν + 1 ) ⁢ Γ ⁡ ( k - 1 2 ⁢ ν + 1 ) , subscript 𝑆 1 𝜈 𝑧 superscript subscript 𝑘 0 superscript 1 𝑘 superscript 1 2 𝑧 2 𝑘 Euler-Gamma 𝑘 1 2 𝜈 1 Euler-Gamma 𝑘 1 2 𝜈 1 {\displaystyle{\displaystyle S_{1}(\nu,z)=\sum_{k=0}^{\infty}\frac{(-1)^{k}(% \tfrac{1}{2}z)^{2k}}{\Gamma\left(k\!+\!\tfrac{1}{2}\nu+1\right)\Gamma\left(k\!% -\!\tfrac{1}{2}\nu\!+\!1\right)},}}
    0 references
    DLMF id
    DLMF:11.10.E10
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1idec
    0 references
    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1idec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4027&oldid=52283"