Verse and Dimensions Wikia
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Verse and Dimensions Wikia


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
Lp 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

Hyperbolic functions and inverses

Hyperbolic sine

Hyperbolic cosine

Hyperbolic tangent

  • Complex hyperbolic tangent (complex map / 3D plot)
    • is elementary
    • is analytic on its domain
    • is meromorphic
    • has simple poles at all
    • is conformal
  • Dual hyperbolic tangent (dual map / 3D plot)
  • Split-complex hyperbolic tangent (split-complex map / 3D plot)
  • Quaternionic hyperbolic tangent ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic hyperbolic tangent ([ vectors] / [ sliders])

Hyperbolic cosecant

  • Complex hyperbolic cosecant (complex map / 3D plot)
    • is elementary
    • is analytic on any open set on its domain
    • is conformal
  • Dual hyperbolic cosecant (dual map / 3D plot)
  • Split-complex hyperbolic cosecant (split-complex map / 3D plot)
  • Quaternionic hyperbolic cosecant ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic hyperbolic cosecant ([ vectors] / [ sliders])

Hyperbolic secant

  • Complex hyperbolic secant (complex map / 3D plot / iterates)
    • is elementary
    • is analytic on any open set on its domain
    • is conformal
  • Dual hyperbolic secant (dual map / 3D plot)
  • Split-complex hyperbolic secant (split-complex map / 3D plot)
  • Quaternionic hyperbolic secant ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic hyperbolic secant ([ vectors] / [ sliders])

Hyperbolic cotangent

  • Complex hyperbolic cotangent (complex map / 3D plot)
    • is elementary
    • is analytic on any open set on its domain
    • is conformal
  • Dual hyperbolic cotangent ([ dual map] / [ 3D plot])
  • Split-complex hyperbolic cotangent ([ split-complex map] / [ 3D plot])
  • Quaternionic hyperbolic cotangent ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic hyperbolic cotangent ([ vectors] / [ sliders])

Inverse hyperbolic sine

  • Complex inverse hyperbolic sine (complex map of principal branch / 3D plot of principal branch / Riemann surface)
    • is elementary
    • is complex analytic
    • is conformal except at and
    • is multivalued
  • Dual inverse hyperbolic sine ([ dual map] / [ 3D plot])
  • Split-complex inverse hyperbolic sine ([ split-complex map] / [ 3D plot])
  • Quaternionic inverse hyperbolic sine ([ vectors] / [ sliders] / [ 3D rotations])
    • is extremely multivalued for elements of
  • Octonionic inverse hyperbolic sine ([ vectors] / [ sliders])
    • is extremely multivalued for elements of

Inverse hyperbolic cosine

  • Complex inverse hyperbolic cosine (complex map of principal branch / 3D plot of principal branch / Riemann surface)
    • is elementary
    • is complex analytic
    • is conformal except at and
    • is multivalued
  • Dual inverse hyperbolic cosine ([ dual map of principal branch] / [ 3D plot of principal branch])
  • Split-complex inverse hyperbolic cosine ([ split-complex map of principal branch] / [ 3D plot of principal branch])
  • Quaternionic inverse hyperbolic cosine ([ vectors] / [ sliders] / [ 3D rotations])
    • is extremely multivalued for elements of
  • Octonionic inverse hyperbolic cosine ([ vectors] / [ sliders])
    • is extremely multivalued for elements of

Inverse hyperbolic tangent

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

Inverse hyperbolic cosecant

  • Complex inverse hyperbolic cosecant (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
    • is multivalued
  • Dual inverse hyperbolic cosecant ([ dual map] / [ 3D plot])
  • Split-complex inverse hyperbolic cosecant ([ split-complex map] / [ 3D plot])
  • Quaternionic inverse hyperbolic cosecant ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic inverse hyperbolic cosecant ([ vectors] / [ sliders])

Inverse hyperbolic secant

  • Complex inverse hyperbolic secant (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
    • is multivalued
  • Dual inverse hyperbolic secant ([ dual map] / [ 3D plot])
  • Split-complex inverse hyperbolic secant ([ split-complex map] / [ 3D plot])
  • Quaternionic inverse hyperbolic secant ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic inverse hyperbolic secant ([ vectors] / [ sliders])

Inverse hyperbolic cotangent

  • Complex inverse hyperbolic cotangent (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
    • is multivalued
  • Dual inverse hyperbolic cotangent ([ dual map] / [ 3D plot])
  • Split-complex inverse hyperbolic cotangent ([ split-complex map] / [ 3D plot])
  • Quaternionic inverse hyperbolic cotangent ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic inverse hyperbolic cotangent ([ vectors] / [ sliders])

Hyperbolic versine

Hyperbolic coversine

Hyperbolic haversine

Hyperbolic excosecant

  • Complex hyperbolic excosecant (complex map / 3D plot)
    • is elementary
    • is analytic on any open set on its domain
    • is conformal
  • Dual hyperbolic excosecant (dual map / 3D plot)
  • Split-complex hyperbolic excosecant (split-complex map / 3D plot)
  • Quaternionic inverse hyperbolic excosecant ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic inverse hyperbolic excosecant ([ vectors] / [ sliders])

Hyperbolic exsecant

  • Complex hyperbolic exsecant (complex map / 3D plot)
    • is elementary
    • is analytic on any open set on its domain
    • is conformal
  • Dual hyperbolic exsecant (dual map / 3D plot)
  • Split-complex hyperbolic exsecant (split-complex map / 3D plot)
  • Quaternionic inverse hyperbolic exsecant ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic inverse hyperbolic exsecant ([ vectors] / [ sliders])

Hyperbolic chord

Inverse hyperbolic versine

Inverse hyperbolic coversine

Inverse hyperbolic haversine

Inverse hyperbolic excosecant

Inverse hyperbolic exsecant

Inverse hyperbolic chord

References

Graphs

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