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Statements
S
(
z
)
=
-
cos
(
1
2
π
z
2
)
∑
n
=
0
∞
(
-
1
)
n
π
2
n
+
1
1
⋅
3
⋯
(
4
n
+
3
)
z
4
n
+
3
+
sin
(
1
2
π
z
2
)
∑
n
=
0
∞
(
-
1
)
n
π
2
n
1
⋅
3
⋯
(
4
n
+
1
)
z
4
n
+
1
.
Fresnel-sine-integral
𝑧
1
2
𝜋
superscript
𝑧
2
superscript
subscript
𝑛
0
superscript
1
𝑛
superscript
𝜋
2
𝑛
1
⋅
1
3
⋯
4
𝑛
3
superscript
𝑧
4
𝑛
3
1
2
𝜋
superscript
𝑧
2
superscript
subscript
𝑛
0
superscript
1
𝑛
superscript
𝜋
2
𝑛
⋅
1
3
⋯
4
𝑛
1
superscript
𝑧
4
𝑛
1
{\displaystyle{\displaystyle S\left(z\right)=-\cos\left(\tfrac{1}{2}\pi z^{2}%
\right)\sum_{n=0}^{\infty}\frac{(-1)^{n}\pi^{2n+1}}{1\cdot 3\cdots(4n+3)}z^{4n%
+3}+\sin\left(\tfrac{1}{2}\pi z^{2}\right)\sum_{n=0}^{\infty}\frac{(-1)^{n}\pi%
^{2n}}{1\cdot 3\cdots(4n+1)}z^{4n+1}.}}
S
(
z
)
Fresnel-sine-integral
𝑧
{\displaystyle{\displaystyle S\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
z
𝑧
{\displaystyle{\displaystyle z}}
n
𝑛
{\displaystyle{\displaystyle n}}
Identifiers
