Fungsi theta asli Jacobi θ1 dengan u = iπz dan dengan nome q = eiπτ = 0.1e0.1iπ . Konvensi adalah (Mathematica): θ

1


(
u
;
q
)



=
2

q


1
4




∑

n
=
0


∞


(
−
1

)

n



q

n
(
n
+
1
)


sin
⁡
(
2
n
+
1
)
u






=

∑

n
=
−
∞


∞


(
−
1

)

n
−


1
2





q



(

n
+


1
2



)


2





e

(
2
n
+
1
)
i
u








{\displaystyle {\begin{aligned}\theta _{1}(u;q)&=2q^{\frac {1}{4}}\sum _{n=0}^{\infty }(-1)^{n}q^{n(n+1)}\sin(2n+1)u\\&=\sum _{n=-\infty }^{\infty }(-1)^{n-{\frac {1}{2}}}q^{\left(n+{\frac {1}{2}}\right)^{2}}e^{(2n+1)iu}\end{aligned}}}