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DLMF:8.12.E5 - MaRDI portal
Statements
e
±
π
i
a
2
i
sin
(
π
a
)
Q
(
-
a
,
z
e
±
π
i
)
=
±
1
2
erfc
(
±
i
η
a
/
2
)
-
i
T
(
a
,
η
)
,
superscript
𝑒
plus-or-minus
𝜋
𝑖
𝑎
2
𝑖
𝜋
𝑎
incomplete-gamma-Q
𝑎
𝑧
superscript
𝑒
plus-or-minus
𝜋
𝑖
plus-or-minus
1
2
complementary-error-function
plus-or-minus
𝑖
𝜂
𝑎
2
𝑖
𝑇
𝑎
𝜂
{\displaystyle{\displaystyle\frac{e^{\pm\pi ia}}{2i\sin\left(\pi a\right)}Q%
\left(-a,ze^{\pm\pi i}\right)=\pm\tfrac{1}{2}\operatorname{erfc}\left(\pm i%
\eta\sqrt{a/2}\right)-iT(a,\eta),}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
erfc
z
complementary-error-function
𝑧
{\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
Γ
(
a
,
z
)
incomplete-Gamma
𝑎
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
Q
(
a
,
z
)
incomplete-gamma-Q
𝑎
𝑧
{\displaystyle{\displaystyle Q\left(\NVar{a},\NVar{z}\right)}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
η
(
λ
)
𝜂
𝜆
{\displaystyle{\displaystyle\eta(\lambda)}}
T
(
a
,
η
)
𝑇
𝑎
𝜂
{\displaystyle{\displaystyle T(a,\eta)}}
Identifiers