Periyodik fonksiyonlar listesi
Düzgün fonksiyonlar

Aksi belirtilmedikçe, listelenen tüm trigonometrik fonksiyonlar  2\pi  periyoduna sahiptir. Aşağıdaki trigonometrik fonksiyonlar için:
| Ad | Sembol | Formül  | Fourier Serileri |
| --- | --- | --- | --- |
| Sinüs |  \sin(x) |  \sum _{n=0}^{\infty }{\frac {(-1)^{n}x^{2n+1}}{(2n+1)!}} |  \sin(x) |
| cas (matematik) |  \operatorname {cas} (x) |  \sin(x)+\cos(x) |  \sin(x)+\cos(x) |
| Kosinüs |  \cos(x) |  \sum _{n=0}^{\infty }{\frac {(-1)^{n}x^{2n}}{(2n)!}} |  \cos(x) |
| cis (matematik) |  e^{ix},\operatorname {cis} (x) |  cos(x) + i sin(x) |  \cos(x)+i\sin(x) |
| Tanjant |  \tan(x) |  {\frac {\sin x}{\cos x}}=\sum _{n=0}^{\infty }{\frac {U_{2n+1}x^{2n+1}}{(2n+1)!}} |  2\sum _{n=1}^{\infty }(-1)^{n-1}\sin(2nx)  |
| Kotanjant |  \cot(x) |  {\frac {\cos x}{\sin x}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}2^{2n}B_{2n}x^{2n-1}}{(2n)!}} |  i+2i\sum _{n=1}^{\infty }(\cos 2nx-i\sin 2nx) [kaynak belirtilmeli] |
| Sekant |  \sec(x) |  {\frac {1}{\cos x}}=\sum _{n=0}^{\infty }{\frac {U_{2n}x^{2n}}{(2n)!}} | - |
| Kosekant |  \csc(x) |  {\frac {1}{\sin x}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n+1}2\left(2^{2n-1}-1\right)B_{2n}x^{2n-1}}{(2n)!}} | - |
| Ekssekant |  \operatorname {exsec} (x) |  \sec(x)-1 | - |
| Ekskosekant |  \operatorname {excsc} (x) |  \csc(x)-1 | - |
| Versinüs |  \operatorname {versin} (x) |  1-\cos(x) |  1-\cos(x) |
| Verkosinüs |  \operatorname {vercosin} (x) |  1+\cos(x) |  1+\cos(x) |
| Koversinüs |  \operatorname {coversin} (x) |  1-\sin(x) |  1-\sin(x) |
| Koverkosinüs |  \operatorname {covercosin} (x) |  1+\sin(x) |  1+\sin(x) |
| Haversinüs |  \operatorname {haversin} (x) |  {\frac {1-\cos(x)}{2}} |  {\frac {1}{2}}-{\frac {1}{2}}\cos(x) |
| Haverkosinüs |  \operatorname {havercosin} (x) |  {\frac {1+\cos(x)}{2}} |  {\frac {1}{2}}+{\frac {1}{2}}\cos(x) |
| Hakoversinüs |  \operatorname {hacoversin} (x) |  {\frac {1-\sin(x)}{2}} |  {\frac {1}{2}}-{\frac {1}{2}}\sin(x) |
| Hakoverkosinüs |  \operatorname {hacovercosin} (x) |  {\frac {1+\sin(x)}{2}} |  {\frac {1}{2}}+{\frac {1}{2}}\sin(x) |
| Jacobi eliptik fonksiyonu sn |  \operatorname {sn} (x,m) |  \sin \operatorname {am} (x,m) |  {\frac {2\pi }{K(m){\sqrt {m}}}}\sum _{n=0}^{\infty }{\frac {q^{n+1/2}}{1-q^{2n+1}}}~\sin {\frac {(2n+1)\pi x}{2K(m)}} |
| Jacobi eliptik fonksiyonu cn |  \operatorname {cn} (x,m) |  \cos \operatorname {am} (x,m) |  {\frac {2\pi }{K(m){\sqrt {m}}}}\sum _{n=0}^{\infty }{\frac {q^{n+1/2}}{1+q^{2n+1}}}~\cos {\frac {(2n+1)\pi x}{2K(m)}} |
| Jacobi eliptik fonksiyonu dn |  \operatorname {dn} (x,m) |  {\sqrt {1-m\operatorname {sn} ^{2}(x,m)}} |  {\frac {\pi }{2K(m)}}+{\frac {2\pi }{K(m)}}\sum _{n=1}^{\infty }{\frac {q^{n}}{1+q^{2n}}}~\cos {\frac {n\pi x}{K(m)}} |
| Jacobi eliptik fonksiyonu zn |  \operatorname {zn} (x,m) |  \int _{0}^{x}dt\left[\operatorname {dn} ^{2}(t,m)-{\frac {E(m)}{K(m)}}\right] |  {\frac {2\pi }{K(m)}}\sum _{n=1}^{\infty }{\frac {q^{n}}{1-q^{2n}}}~\sin {\frac {n\pi x}{K(m)}} |
| Weierstrass eliptik fonksiyonu |  \wp (x,\Lambda ) |  {\frac {1}{x^{2}}}+\sum _{\lambda \in \Lambda -\{0\}}\left[{\frac {1}{(x-\lambda )^{2}}}-{\frac {1}{\lambda ^{2}}}\right] |   |
| Clausen fonksiyonu |  \operatorname {Cl} _{2}(x) |  -\int _{0}^{x}\ln \left|2\sin {\frac {x}{2}}\right|dx |  \sum _{k=1}^{\infty }{\frac {\sin kx}{k^{2}}} |