hyperbolic identities
There are many formulas involving hyperbolic functions, many of which are to formulas for trigonometric functions
. Below is a list of some of these formulas (usually for real arguments
).
- 1.
Hyperbolic version of Pythagorean identities
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- 2.
Fractional identities
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- 3.
Hyperbolic functions of a purely imaginary number
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- 4.
Addition formulas
and subtraction formulas (http://planetmath.org/AdditionAndSubtractionFormulasForHyperbolicFunctions)
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- 5.
Formulas for hyperbolic functions of a complex number
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- 6.
Opposite formulas
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- 7.
Double argument formulas
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- 8.
Periodicity (http://planetmath.org/Periodic) formulas
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Cf (http://planetmath.org/Cf). the periodicity of exponential function
.
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- 9.
Exponential formulas (http://planetmath.org/ExponentialFunction)
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Note that the first three formulas given in this are definitions.
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Title | hyperbolic identities |
Canonical name | HyperbolicIdentities |
Date of creation | 2013-03-22 17:50:42 |
Last modified on | 2013-03-22 17:50:42 |
Owner | Wkbj79 (1863) |
Last modified by | Wkbj79 (1863) |
Numerical id | 11 |
Author | Wkbj79 (1863) |
Entry type | Topic |
Classification | msc 33B10 |
Classification | msc 26A09 |
Synonym | hyperbolic formulas |
Synonym | hyperbolic formulae |
Related topic | GoniometricFormulae |
Related topic | AdditionAndSubtractionFormulasForHyperbolicFunctions |
Related topic | ExamplesOfPeriodicFunctions |
Related topic | TaylorSeriesOfHyperbolicFunctions |