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

Polynomials, Rationals, Exponentials, and Logarithms

Square

Cube

Tesseract

  • Complex tesseract (complex map v1 / complex map v2 / 3D plot / domain colouring / contour plot / Mandelbrot)
    • is elementary
    • is complex analytic
    • has a zero of order 4 at
    • has a pole of order 4 at
    • is conformal except at
    • is entire
  • Dual tesseract ([ dual map] / [ 3D plot])
  • Split-complex tesseract ([ split-complex map] / [ 3D plot])
  • Quaternionic tesseract ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic tesseract ([ vectors] / [ sliders])

Constant functions

Linear functions

  • Complex linear functions (complex map / polygons in the Euclidean plane / 3D plot / [ sliders] / [ domain colouring] / [ contour plot])
  • Dual linear functions ([ dual map] / [ 3D plot] / [ sliders])
  • Split-complex linear functions ([ split-complex map] / [ 3D plot] / [ sliders])
  • Quaternionic linear functions ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic linear functions ([ vectors] / [ sliders])

Linear fractions

Quadratic functions

  • Complex quadratic functions (complex map / 3D plot / [ sliders] / [ domain colouring] / [ contour plot])
  • Dual quadratic functions ([ dual map] / [ 3D plot] / [ sliders])
  • Split-complex quadratic functions ([ split-complex map] / [ 3D plot] / [ sliders])
  • Quaternionic quadratic functions ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic quadratic functions ([ vectors] / [ sliders])

Cubic functions

  • Complex cubic functions (complex map / 3D plot / [ sliders] / [ domain colouring] / [ contour plot])
  • Dual cubic functions ([ dual map] / [ 3D plot] / [ sliders])
  • Split-complex cubic functions ([ split-complex map] / [ 3D plot] / [ sliders])
  • Quaternionic cubic functions ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic cubic functions ([ vectors] / [ sliders])

Quartic functions

  • Complex quartic functions ([ complex map] / 3D plot / [ sliders] / [ domain colouring] / [ contour plot])
  • Dual quartic functions ([ dual map] / [ 3D plot] / [ sliders])
  • Split-complex quartic functions ([ split-complex map] / [ 3D plot] / [ sliders])
  • Quaternionic quartic functions ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic quartic functions ([ vectors] / [ sliders])

Exponentiation

Square root

Cube root

Tesseract root

Roots

Exponential

Natural logarithm

Binary logarithm

Decimal logarithm

Quater-imaginary logarithm

Logarithms

Exponential minus one

Natural logarithm one plus

Periexp

  • Complex periexp (complex map of principal branch / 3D plot of principal branch / Riemann surface / [ domain colouring] / [ contour plot])
    • is elementary
    • is analytic on any open set on its domain
    • has a simple pole at
    • is conformal
    • is multivalued
    • has a branch point at 0
  • Quaternionic periexp ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic periexp ([ vectors] / [ sliders])

Gaussian functions

  • Complex Gaussian functions (complex map / 3D plot / [ sliders] / [ domain colouring] / [ contour plot])
  • Dual Gaussian functions ([ dual map] / [ 3D plot] / [ sliders])
  • Split-complex Gaussian functions ([ split-complex map] / [ 3D plot] / [ sliders])
  • Quaternionic Gaussian functions ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic Gaussian functions ([ vectors] / [ sliders])

Lorentzian functions

Trappmann function

Zex

Zog

  • Complex zog (complex map of principal branch / complex maps of branches / 3D plot of principal branch / Riemann surface / [ domain colouring] / [ contour plot])
    • is elementary
    • is complex analytic
    • is conformal except at and
    • is multivalued
    • has a branch point at
  • Dual zog ([ dual map] / [ 3D plot])
  • Split-complex zog ([ split-complex map] / [ 3D plot])
  • Quaternionic zog ([ vectors] / [ sliders] / [ 3D rotations])
    • is extremely multivalued for elements of
  • Octonionic zog ([ vectors] / [ sliders])
    • is extremely multivalued for elements of

Keller function

  • Complex Keller function (complex map of principal branch / 3D plot of principal branch / Riemann surface / [ domain colouring] / [ contour plot])
  • Dual Keller function ([ dual map] / [ 3D plot])
  • Split-complex Keller function ([ split-complex map] / [ 3D plot])
  • Quaternionic Keller function ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic Keller function ([ vectors] / [ sliders])

Inverse Keller function

  • Complex inverse Keller function (complex map of principal branch / 3D plot of principal branch / Riemann surface / [ domain colouring] / [ contour plot])
  • Dual inverse Keller function ([ dual map] / [ 3D plot])
  • Split-complex inverse Keller function ([ split-complex map] / [ 3D plot])
  • Quaternionic inverse Keller function ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic inverse Keller function ([ vectors] / [ sliders])

Shoka function

  • Complex Shoka function (complex map of principal branch / 3D plot of principal branch / Riemann surface / [ domain colouring] / [ contour plot])
  • Dual Shoka function ([ dual map] / [ 3D plot])
  • Split-complex Shoka function ([ split-complex map] / [ 3D plot])
  • Quaternionic Shoka function ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic Shoka function ([ vectors] / [ sliders])

Inverse Shoka function

  • Complex inverse Shoka function (complex map of principal branch / 3D plot of principal branch / Riemann surface / [ domain colouring] / [ contour plot])
  • Dual inverse Shoka function ([ dual map] / [ 3D plot])
  • Split-complex inverse Shoka function ([ split-complex map] / [ 3D plot])
  • Quaternionic inverse Shoka function ([ vectors] / [ sliders] / [ 3D rotations])
  • Octonionic inverse Shoka function ([ vectors] / [ sliders])

Inverse Tania function

  • Complex inverse Tania function (complex map of principal branch / 3D plot of principal branch / Riemann surface / [ domain colouring] / [ contour plot])
    • is elementary
    • is analytic on any open set on its domain
    • is conformal except at
    • is multivalued
    • has a branch point at
  • Dual inverse Tania function ([ dual map] / [ 3D plot])
  • Split-complex inverse Tania function ([ split-complex map] / [ 3D plot])
  • Quaternionic inverse Tania function ([ vectors] / [ sliders] / [ 3D rotations])
    • is extremely multivalued for elements of
  • Octonionic inverse Tania function ([ vectors] / [ sliders])
    • is extremely multivalued for elements of

Anka function

References

Graphs

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