Documentation

This is machine translation

Translated by Microsoft
Mouse over text to see original. Click the button below to return to the English verison of the page.

Si

Sine integral function

MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

Syntax

Si(x)

Description

Si(x) represents the sine integral 0xsin(t)tdt.

If x is a floating-point number, then Si(x) returns floating-point results. The special values Si(0) = 0, Si(∞) = π/2, and Si(-∞) = -π/2 are implemented. For all other arguments, Si returns symbolic function calls.

If x is a negative integer or a negative rational number, then Si(x) = -Si(-x). The Si function also uses this reflection rule when the argument is a symbolic product involving such a factor. See Example 2.

The float attribute of Si is a kernel function, thus, floating-point evaluation is fast.

Environment Interactions

When called with a floating-point argument, the functions are sensitive to the environment variable DIGITS which determines the numerical working precision.

Examples

Example 1

Most calls with exact arguments return themselves unevaluated:

Si(0), Si(1), Si(sqrt(2)), Si(x + 1), Si(infinity)

To approximate exact results with floating-point numbers, use float:

float(Si(1)), float(Si(sqrt(2)))

Alternatively, use a floating-point value as an argument:

Si(-5.0), Si(1.0), Si(2.0 + 10.0*I)

Example 2

For negative real numbers and products involving such numbers, Si applies the reflection rule Si(-x) = -Si(x):

Si(-3), Si(-3/7), Si(-sqrt(2)), Si(-x/7), Si(-0.3*x)

No such "normalization" occurs for complex numbers or arguments that are not products:

Si(- 3 - I), Si(3 + I), Si(x - 1), Si(1 - x)

Example 3

diff, float, limit, series, and other functions handle expressions involving Si:

diff(Si(x), x, x, x), float(ln(3 + Si(sqrt(PI))))

limit(Si(2*x^2/(1+x)), x = infinity)

series(Si(x), x = 0)

series(Si(x), x = infinity, 3)

Parameters

x

An arithmetical expression

Return Values

Arithmetical expression.

Overloaded By

x

Algorithms

Si, Ssi, and Shi are entire functions.

Ssi(x) = Si(x) - π for all x in the complex plane.

i*Si(x) = Shi(i*x) for all x in the complex plane.

Reference: M. Abramowitz and I. Stegun, "Handbook of Mathematical Functions", Dover Publications Inc., New York (1965).

See Also

MuPAD Functions

Was this topic helpful?