fresnelS

The Fresnel sine integral function

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

fresnelS(z)

Description

fresnelS(z) = .

The function S = fresnelS is analytic throughout the complex plane. It satisfies fresnelS(-z) = -fresnelS(z), fresnelS(conjugate(z)) = conjugate(fresnelS(z)), fresnelS(I*z) =-I*fresnelS(z) for all complex values of z.

fresnelS(z) returns special values for z = 0, , and . Symbolic function calls are returned for all other symbolic values of z. In the graphical user interface of MuPAD® symbolic function calls are typeset as fresnelS(z) = .

When called with floating-point arguments, the function returns floating-point values.

With simplify and Simplify, the reflection rule fresnelS(-z) = -fresnelS(z) is used to create a "normal form" of symbolic function calls. Cf. Example 3.

Environment Interactions

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

Examples

Example 1

We call the Fresnel functions with various arguments: Symbolic calls are typeset as fresnelC(z) = and fresnelS(z) = , respectively:

fresnelC(0),
fresnelC(1),
fresnelC(PI + I),
fresnelC(z),
fresnelC(infinity)

fresnelS(0), 
fresnelS(1),
fresnelS(PI + I),
fresnelS(z),
fresnelS(infinity)

Floating point values are returned for floating-point arguments:

fresnelC(1.0),
fresnelC(float(PI)),
fresnelS(-3.45 + 0.75*I)

Example 2

The functions diff, float, limit, and series handle expressions involving the Fresnel functions:

diff(fresnelC(x), x),
diff(fresnelS(x), x)

float(fresnelC(PI)),
float(fresnelS(-100))

limit(fresnelC(x), x = infinity),
limit(fresnelS(x), x = -infinity)

series(fresnelC(x), x = 0),
series(fresnelS(x), x = infinity, 4)

Example 3

With simplify and Simplify, the reflection rules fresnelC(-z) = -fresnelC(z) and fresnelS(-z) = -fresnelS(z) are used to create a "normal form" of symbolic function calls:

Simplify(fresnelC(1 - x)),
Simplify(fresnelC(x - 1))

3*fresnelS(z) + 2*fresnelS(-z)

Simplify(%)

Parameters

z

An arithmetical expression

Return Values

Arithmetical expression.

Overloaded By

z

See Also

MuPAD Functions

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