ℍ𝕪𝕡𝕖𝕣𝕔𝕠𝕞𝕡𝕝𝕖𝕩 𝕤𝕥𝕦𝕗𝕗

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Navigation

Functions of a hypercomplex variable

Structures

Number systems

Shapes

Special constants

Sets of functions

Functions of functions

Generalized Mandelbrot sets and Julia sets

Generalized Cauchy-Riemann equations

Full page

Recreational monocosm

WIP

thingy about multidimensional numbers or something

Complex map of $\zeta ({\frac {1}{2}}+{\acute {i}}t)$ where $t\in [0,75]$.

Complex ${\rm {cheta}}(z)$ domain colouring.

Navigation

• Multiplication
• Spacetime globes (classical and special relativity)
  • Penrose diagrams (split-complex maps / contour plots)
• Generalized polygons
• Stereographic projection of a sphere
  • Stereographic projection of Earth's night sky
• Euclidean plane
• Poincaré disc and half-plane models of the hyperbolic plane
• Map projections of Earth
  • Equirectangular projections (plate carrée, Cassini projection)
  • Transverse Mercator projection (complex maps / contour plots)
  • Littrow projection (complex maps / contour plots)
• Elliptic curves
• Tetration (portal)
• Solar System
• Colourimetric functions
  • Chromaticity diagrams
• Planck's law
• Stellar temperature colours
• Stellar evolution
• Relativistic Doppler shifting
• Star size from luminosity and temperature
• Taxicab geometry
• Chebyshev geometry
• Gamma function
• Factorials (portal)
• Zeta function (zeros)
• Mandelbrot set
• Julia sets
• Recreational monocosm

Functions of a hypercomplex variable

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

Posts (in ideal reading order)

• Part I: Cursory overview of familiar territory
  • Visualizing complex functions
• Part II: Split-complex and Dual numbers
• The Family
• Extremely multivalued functions
• Tetration Portal
• Factorial Portal
• Zeros of the Riemann zeta function
• Function list (alphabetical)
• Special function evaluations and approximations used
• Pseudogons, Complexgons, and more
  • Schläflians of polytopes
  • Generalized Cartan matrices of complex polytopes
  • Apeirogons
• Astronomy Portal
• Stellar evolution