hyperbolic sine integral
The function hyperbolic sine integral (in Latin sinus hyperbolicus integralis) from to is defined as
(1) |
or alternatively as
It isn’t an elementary function. The equation (1) implies the Taylor series expansion
which converges for all complex values and thus defines an entire transcendental function. Using the Taylor expansions, it is easily seen that
connects Shi to the sine integral function.
satisfies the linear third differential equation
Title | hyperbolic sine integral |
---|---|
Canonical name | HyperbolicSineIntegral |
Date of creation | 2013-03-22 18:27:48 |
Last modified on | 2013-03-22 18:27:48 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 7 |
Author | pahio (2872) |
Entry type | Definition |
Classification | msc 30A99 |
Synonym | Shi |
Related topic | HyperbolicFunctions |
Related topic | SineIntegral |