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

Trigonometric functions and inverses

Sine

Cosine

Tangent

Cosecant

  • Complex cosecant (complex map / 3D plot)
    • is elementary
    • is analytic on any open set on its domain
    • has simple poles at all
    • has an essential singularity at
    • is conformal
  • Dual cosecant (dual map / 3D plot)
  • Split-complex cosecant (split-complex map / 3D plot)
  • Quaternionic cosecant ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic cosecant ([ vectors] / [ sliders])

Secant

  • Complex secant (complex map / 3D plot / iterates)
    • is elementary
    • is analytic on any open set on its domain
    • has simple poles at all
    • has an essential singularity at
    • is conformal
  • Dual secant (dual map / 3D plot)
  • Split-complex secant (split-complex map / 3D plot)
  • Quaternionic secant ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic secant ([ vectors] / [ sliders])

Cotangent

  • Complex cotangent (complex map / 3D plot)
    • is elementary
    • is analytic on any open set on its domain
    • has simple poles at all
    • has an essential singularity at
    • is conformal
  • Dual cotangent (dual map / 3D plot)
  • Split-complex cotangent (split-complex map / 3D plot)
  • Quaternionic cotangent ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic cotangent ([ vectors] / [ sliders])

Cis

  • Complex cis (complex map / 3D plot)
    • is elementary
    • is complex analytic
    • is conformal
    • is entire

Cocis

  • Complex cocis (complex map / 3D plot)
    • is elementary
    • is complex analytic
    • is conformal
    • is entire

Inverse sine

Inverse cosine

Inverse tangent

Inverse cosecant

  • Complex inverse cosecant (complex map of principal branch / 3D plot of principal branch / Riemann surface)
    • is elementary
    • is analytic everywhere in its domain except at and
    • is conformal except at and
    • is multivalued
    • has branch points at and
  • Dual inverse cosecant ([ dual map of principal branch] / [ 3D plot of principal branch])
  • Split-complex inverse cosecant ([ split-complex map of principal branch] / [ 3D plot of principal branch])
  • Quaternionic inverse cosecant ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic inverse cosecant ([ vectors] / [ sliders])

Inverse secant

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

Inverse cotangent

  • Complex inverse 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 cotangent ([ dual map of principal branch] / [ 3D plot of principal branch])
  • Split-complex inverse cotangent ([ split-complex map of principal branch] / [ 3D plot of principal branch])
  • Quaternionic inverse cotangent ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic inverse cotangent ([ vectors] / [ sliders])

Inverse cis

Inverse cocis

Versine

  • Complex versine (complex map / 3D plot)
    • is elementary
    • is complex analytic
    • is conformal except at elements of
    • is entire
  • Dual versine (dual map / 3D plot)
  • Split-complex versine (split-complex map / 3D plot)
  • Quaternionic versine ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic versine ([ vectors] / [ sliders])

Coversine

  • Complex coversine (complex map / 3D plot)
    • is elementary
    • is complex analytic
    • is conformal except at elements of
    • is entire
  • Dual coversine (dual map / 3D plot)
  • Split-complex coversine (split-complex map / 3D plot)
  • Quaternionic coversine ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic coversine ([ vectors] / [ sliders])

Haversine

  • Complex haversine (complex map / 3D plot)
    • is elementary
    • is complex analytic
    • is conformal except at elements of
    • is entire
  • Dual haversine (dual map / 3D plot)
  • Split-complex haversine (split-complex map / 3D plot)
  • Quaternionic haversine ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic haversine ([ vectors] / [ sliders])

Excosecant

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

Exsecant

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

Chord

  • Complex chord ([ complex map] / [ 3D plot])
    • is elementary
    • is complex analytic
    • is conformal
  • Dual chord ([ dual map] / [ 3D plot])
  • Split-complex chord ([ split-complex map] / [ 3D plot])
  • Quaternionic chord ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic chord ([ vectors] / [ sliders])

Inverse versine

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

Inverse coversine

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

Inverse haversine

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

Inverse excosecant

  • Complex inverse excosecant (complex map of principal branch / 3D plot of principal branch / Riemann surface)
    • is elementary
    • is analytic everywhere in its domain except at and
    • is conformal except at and
    • is multivalued
    • has branch points at and
  • Dual inverse excosecant ([ dual map of principal branch] / [ 3D plot of principal branch])
  • Split-complex inverse excosecant ([ split-complex map of principal branch] / [ 3D plot of principal branch])
  • Quaternionic inverse excosecant ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic inverse excosecant ([ vectors] / [ sliders])

Inverse exsecant

  • Complex inverse exsecant (complex map of principal branch / 3D plot of principal branch / Riemann surface)
    • is elementary
    • is analytic everywhere in its domain except at and
    • is conformal except at and
    • is multivalued
    • has branch points at and
  • Dual inverse exsecant ([ dual map of principal branch] / [ 3D plot of principal branch])
  • Split-complex inverse exsecant ([ split-complex map of principal branch] / [ 3D plot of principal branch])
  • Quaternionic inverse exsecant ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic inverse exsecant ([ vectors] / [ sliders])

Inverse chord

  • Complex inverse chord ([ complex map of principal branch] / [ 3D plot of principal branch] / [ Riemann surface])
    • is elementary
    • is analytic everywhere in its domain except at and
    • is conformal except at and
    • is multivalued
    • has branch points at and
  • Dual inverse chord ([ dual map of principal branch] / [ 3D plot of principal branch])
  • Split-complex inverse chord ([ split-complex map of principal branch] / [ 3D plot of principal branch])
  • Quaternionic inverse chord ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic inverse chord ([ vectors] / [ sliders])

Schläflian function

  • Complex polygonal Schläflian function (complex map / 3D plot)
    • is elementary
    • is analytic everywhere in its domain
    • is conformal except at elements of
    • is multivalued
  • Dual polygonal Schläflian function ([ dual map] / [ 3D plot])
  • Split-complex polygonal Schläflian function ([ split-complex map] / [ 3D plot])
  • Quaternionic polygonal Schläflian function ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic polygonal Schläflian function ([ vectors] / [ sliders])

References

Graphs

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