sine integral
The function sine integral (in Latin sinus integralis) from to is defined as
(1) |
or alternatively as
It isn’t an elementary function. The equation (1) implies the Taylor series
which converges for all complex values and thus defines an entire transcendental function.
satisfies the linear third differential equation
Remark 1.
Remark 2. There is also another “sine integral”
and the corresponding cosine integral
where is the Euler–Mascheroni constant (http://planetmath.org/EulerMascheroniConstant).
Title | sine integral |
Canonical name | SineIntegral |
Date of creation | 2015-02-04 12:58:26 |
Last modified on | 2015-02-04 12:58:26 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 17 |
Author | pahio (2872) |
Entry type | Definition |
Classification | msc 30A99 |
Synonym | sinus integralis |
Synonym | Si |
Related topic | SincFunction |
Related topic | SineIntegralInInfinity |
Related topic | LogarithmicIntegral2 |
Related topic | CurvatureOfNielsensSpiral |
Related topic | LaplaceTransformOfIntegralSine |
Related topic | FresnelIntegrals |
Related topic | HyperbolicSineIntegral |
Defines | sine integral |
Defines | sinus integralis |
Defines | cosine integral |