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

## 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 