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Statements
F
(
a
,
b
c
+
λ
;
z
)
∼
Γ
(
c
+
λ
)
Γ
(
c
-
b
+
λ
)
∑
s
=
0
∞
q
s
(
z
)
(
b
)
s
λ
-
s
-
b
,
asymptotic-expansion
Gauss-hypergeometric-F
𝑎
𝑏
𝑐
𝜆
𝑧
Euler-Gamma
𝑐
𝜆
Euler-Gamma
𝑐
𝑏
𝜆
superscript
subscript
𝑠
0
subscript
𝑞
𝑠
𝑧
Pochhammer
𝑏
𝑠
superscript
𝜆
𝑠
𝑏
{\displaystyle{\displaystyle F\left({a,b\atop c+\lambda};z\right)\sim\frac{%
\Gamma\left(c+\lambda\right)}{\Gamma\left(c-b+\lambda\right)}\sum_{s=0}^{%
\infty}q_{s}(z){\left(b\right)_{s}}\lambda^{-s-b},}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
F
(
a
,
b
;
c
;
z
)
Gauss-hypergeometric-F
𝑎
𝑏
𝑐
𝑧
{\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
(
a
)
n
Pochhammer
𝑎
𝑛
{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
s
𝑠
{\displaystyle{\displaystyle s}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
b
𝑏
{\displaystyle{\displaystyle b}}
c
𝑐
{\displaystyle{\displaystyle c}}
q
s
(
z
)
subscript
𝑞
𝑠
𝑧
{\displaystyle{\displaystyle q_{s}(z)}}
Identifiers
