Documentation

Ssi

Shifted sine integral function

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

Ssi(x)

Description

Ssi(x) represents the shifted sine integral Si(x)π2.

The special values Ssi(0) = -π/2, Ssi(∞) = 0, Ssi(- ∞) = -π are implemented.

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

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:

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

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

float(Ssi(1)), float(Ssi(sqrt(2)))

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

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

Example 2

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

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

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

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

Example 3

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

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

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

series(Ssi(x), x = 0)

series(Ssi(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.

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

See Also

MuPAD Functions

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