Osborne's Rule
The prescription that a Trigonometry identity can be converted to an analogous identity for Hyperbolic Functionsby expanding, exchanging trigonometric functions with their hyperbolic counterparts, and then flipping the sign of each terminvolving the product of two Hyperbolic Sines. For example, given the identity
Osborne's rule gives the corresponding identity
See also Hyperbolic Functions, Trigonometry
- Euler's Displacement Theorem
- Euler's Distribution Theorem
- Euler's Factorization Method
- Euler's Finite Difference Transformation
- Euler's Graeco-Roman Squares Conjecture
- Euler's Homogeneous Function Theorem
- Euler's Hypergeometric Transformations
- Euler's Idoneal Number
- Euler's Machin-Like Formula
- Euler's Pentagonal Number Theorem
- Euler's Phi Function
- Euler's Polygon Division Problem
- Euler's Quadratic Residue Theorem
- Euler Square
- Euler's Rotation Theorem
- Euler's Rule
- Euler's Series Transformation
- Euler's Spiral
- Euler's Sum of Powers Conjecture
- Euler's Theorem
- Euler's Totient Rule
- Euler's Transform
- Euler's Triangle
- Euler Sum
- Euler Totient Function