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DLMF:18.15.E25
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Formula:6417
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MaRDI QID
Q6417
Label: DLMF:18.15.E25
Digital Library of Mathematical Functions ID
18.15.E25
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}}}
Constraint(s)
Symbols List
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
: gamma function
n
𝑛
{\displaystyle{\displaystyle n}}
: nonnegative integer
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