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DLMF:20.11.E9
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Formula:7545
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MaRDI QID
Q7545
Label: DLMF:20.11.E9
Digital Library of Mathematical Functions ID
20.11.E9
φ
m
,
n
(
z
,
q
)
=
φ
m
,
1
(
z
,
q
)
φ
1
,
n
(
z
,
q
)
=
1
φ
n
,
m
(
z
,
q
)
=
φ
m
,
1
(
z
,
q
)
φ
n
,
1
(
z
,
q
)
=
φ
1
,
n
(
z
,
q
)
φ
1
,
m
(
z
,
q
)
.
Jacobi-theta-combined
𝑚
𝑛
𝑧
𝑞
Jacobi-theta-combined
𝑚
1
𝑧
𝑞
Jacobi-theta-combined
1
𝑛
𝑧
𝑞
1
Jacobi-theta-combined
𝑛
𝑚
𝑧
𝑞
Jacobi-theta-combined
𝑚
1
𝑧
𝑞
Jacobi-theta-combined
𝑛
1
𝑧
𝑞
Jacobi-theta-combined
1
𝑛
𝑧
𝑞
Jacobi-theta-combined
1
𝑚
𝑧
𝑞
{\displaystyle{\displaystyle\varphi_{m,n}\left(z,q\right)=\varphi_{m,1}\left(z% ,q\right)\varphi_{1,n}\left(z,q\right)=\frac{1}{\varphi_{n,m}\left(z,q\right)}% =\frac{\varphi_{m,1}\left(z,q\right)}{\varphi_{n,1}\left(z,q\right)}=\frac{% \varphi_{1,n}\left(z,q\right)}{\varphi_{1,m}\left(z,q\right)}.}}
Constraint(s)
Symbols List
φ
n
,
m
(
z
,
q
)
Jacobi-theta-combined
𝑛
𝑚
𝑧
𝑞
{\displaystyle{\displaystyle\varphi_{\NVar{n},\NVar{m}}\left(\NVar{z},\NVar{q}% \right)}}
:
m
𝑚
{\displaystyle{\displaystyle m}}
: integer
n
𝑛
{\displaystyle{\displaystyle n}}
: integer
z
𝑧
{\displaystyle{\displaystyle z}}
: complex
q
𝑞
{\displaystyle{\displaystyle q}}
: nome
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