Arithmetic |
Hypercomplex components |
Polynomials, Rationals, Exponentials, and Logarithms |
Trigonometric functions and inverses |
Hyperbolic functions and inverses |

Sinc analogues |
Logistic functions, Gudermannian, and inverses |
Algebraic curves |
Bessel-type functions |
Integer functions |

Factorials and binomial coefficient |
Productlogarithms, hyperoperators, and relatives |
Physical functions |
L^{p} trigonometric functions |
Exponential integral and relatives |

Elliptic integrals and relatives |
Gamma functions and relatives |
Error functions and relatives |
Zeta functions, Polylogarithms, and relatives |
Modular forms and relatives |

## Functions of a hypercomplex variable

### Logistic functions, Gudermannian, and inverses

#### Sigmoid function

- Complex sigmoid (complex map / 3D plot)
- is elementary
- is complex analytic
- is conformal

- Dual sigmoid (dual map / 3D plot)
- Split-complex sigmoid (split-complex map / 3D plot)
- Quaternionic sigmoid ([ vectors] / [ sliders] / [ 3D rotations])
- Octonionic sigmoid ([ vectors] / [ sliders])

#### Logistic functions

- Complex logistics (complex map / 3D plot)
- Dual logistics ([ dual map] / [ 3D plot])
- Split-complex logistics ([ split-complex map] / [ 3D plot])
- Quaternionic logistics ([ vectors] / [ sliders] / [ 3D rotations])
- Octonionic logicstics ([ vectors] / [ sliders])

#### Gudermannian

- Complex Gudermannian (complex map of principal branch / 3D plot of principal branch / Riemann surface)
- is elementary
- is analytic on any open set on its domain
- is conformal

- Dual Gudermannian ([ dual map] / [ 3D plot])
- Split-complex Gudermannian ([ split-complex map] / [ 3D plot])
- Quaternionic Gudermannian ([ vectors] / [ sliders] / [ 3D rotations])
- Octonionic Gudermannian ([ vectors] / [ sliders])

#### Logit

- Complex logit (complex map of principal branch / 3D plot of principal branch / Riemann surface)
- is elementary
- is analytic on any open set on its domain
- is conformal

- Dual logit (dual map / 3D plot)
- Split-complex logit (split-complex map / 3D plot)
- Quaternionic logit ([ vectors] / [ sliders] / [ 3D rotations])
- is extremely multivalued for elements of

- Octonionic logit ([ vectors] / [ sliders])
- is extremely multivalued for elements of

#### Inverse Gudermannian

- Complex inverse Gudermannian (complex map of principal branch / 3D plot of principal branch / Riemann surface)
- is elementary
- is analytic on any open set on its domain
- is conformal

- Dual inverse Gudermannian ([ dual map] / [ 3D plot])
- Split-complex inverse Gudermannian ([ split-complex map] / [ 3D plot])
- Quaternionic inverse Gudermannian ([ vectors] / [ sliders] / [ 3D rotations])
- is extremely multivalued for elements of

- Octonionic inverse Gudermannian ([ vectors] / [ sliders])
- is extremely multivalued for elements of