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DLMF:18.15.E25 - MaRDI portal

DLMF:18.15.E25 (Q6417)

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DLMF:18.15.E25
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    Statements

    DLMF defining formula
    λ n = { Γ ⁡ ( n + 1 ) / Γ ⁡ ( 1 2 ⁢ n + 1 ) , n ⁢  even , Γ ⁡ ( n + 2 ) / ( μ 1 2 ⁢ Γ ⁡ ( 1 2 ⁢ n + 3 2 ) ) , n ⁢  odd , subscript 𝜆 𝑛 cases Euler-Gamma 𝑛 1 Euler-Gamma 1 2 𝑛 1 𝑛  even Euler-Gamma 𝑛 2 superscript 𝜇 1 2 Euler-Gamma 1 2 𝑛 3 2 𝑛  odd {\displaystyle{\displaystyle\lambda_{n}=\begin{cases}\ifrac{\Gamma\left(n+1% \right)}{\Gamma\left(\frac{1}{2}n+1\right)},&n\text{ even},\\ \ifrac{\Gamma\left(n+2\right)}{\left(\mu^{\frac{1}{2}}\Gamma\left(\frac{1}{2}n% +\frac{3}{2}\right)\right)},&n\text{ odd},\end{cases}}}
    0 references
    Symbols used
    gamma function
    DLMF defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1odec
    0 references

    Identifiers

     
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