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Everything about Hyperbolic functions

Hyperbolic analogues of trigonometric functions

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola. Also, similarly to how the derivatives of sin(t) and cos(t) are cos(t) and –sin(t), the derivatives of sinh(t) and cosh(t) are cosh(t) and sinh(t). Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Hyperbolic functionsA 5-minute orientation
  2. Skim a recent paper: Neural network operators with hyperbolic tangent functionsInfluential work since 2022
  3. Pick up a classic book: Automorphisms of surfaces after Nielsen and ThurstonThe most-reprinted book on the subject
  4. Read the landmark paper: Spectral functions and zeta functions in hyperbolic spacesCited 157 times
  5. Go sideways: Trigonometric functionsA closely related topic
  6. Go sideways: Hyperbolic triangleA closely related topic

📖 Definitions

Noun plural of hyperbolic function

🗂️ The subject at a glance

  1. History
  2. Notation
  3. Definitions
  4. Characterizing properties
  5. Useful relations
  6. Inverse functions as logarithms
  7. Derivatives
  8. Second derivatives
  9. Standard integrals
  10. Taylor series expressions
  11. Infinite products and continued fractions
  12. Comparison with circular functions

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics