Mathematical Research Data Initiative
Main page
Recent changes
Random page
SPARQL
MaRDI@GitHub
In other projects
MaRDI portal item
Discussion
View source
View history
Purge
English
Log in
Formula
:
6052
From MaRDI portal
Jump to:
navigation
,
search
Digital Library of Mathematical Functions ID
17.4.E6
Φ
(
2
)
(
a
;
b
,
b
′
;
c
,
c
′
;
q
;
x
,
y
)
=
∑
m
,
n
≥
0
(
a
;
q
)
m
+
n
(
b
;
q
)
m
(
b
′
;
q
)
n
x
m
y
n
(
q
;
q
)
m
(
q
;
q
)
n
(
c
;
q
)
m
(
c
′
;
q
)
n
,
q-Appell-Phi-2
𝑎
𝑏
superscript
𝑏
′
𝑐
superscript
𝑐
′
𝑞
𝑥
𝑦
subscript
𝑚
𝑛
0
q-Pochhammer-symbol
𝑎
𝑞
𝑚
𝑛
q-Pochhammer-symbol
𝑏
𝑞
𝑚
q-Pochhammer-symbol
superscript
𝑏
′
𝑞
𝑛
superscript
𝑥
𝑚
superscript
𝑦
𝑛
q-Pochhammer-symbol
𝑞
𝑞
𝑚
q-Pochhammer-symbol
𝑞
𝑞
𝑛
q-Pochhammer-symbol
𝑐
𝑞
𝑚
q-Pochhammer-symbol
superscript
𝑐
′
𝑞
𝑛
{\displaystyle{\displaystyle\Phi^{(2)}\left(a;b,b^{\prime};c,c^{\prime};q;x,y% \right)=\sum_{m,n\geq 0}\frac{\left(a;q\right)_{m+n}\left(b;q\right)_{m}\left(% b^{\prime};q\right)_{n}x^{m}y^{n}}{\left(q;q\right)_{m}\left(q;q\right)_{n}% \left(c;q\right)_{m}\left(c^{\prime};q\right)_{n}},}}
Constraint(s)
Symbols List
(
a
;
q
)
n
q-Pochhammer-symbol
𝑎
𝑞
𝑛
{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
:
q
𝑞
{\displaystyle{\displaystyle q}}
: complex base
m
𝑚
{\displaystyle{\displaystyle m}}
: nonnegative integer
n
𝑛
{\displaystyle{\displaystyle n}}
: nonnegative integer
x
𝑥
{\displaystyle{\displaystyle x}}
: real variable
y
𝑦
{\displaystyle{\displaystyle y}}
: real variable
Resources that cite this formula
No records found.
Tools
What links here
Related changes
Special pages
Printable version
Permanent link
Page information