Documentation

fresnelC

The Fresnel cosine integral function

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

fresnelC(z)

Description

fresnelC(z) = 0zcos(πt22)dt.

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

fresnelC(z) returns special values for z = 0, z = ±∞, and z = ±i∞. Symbolic function calls are returned for all other symbolic values of z. In a MuPAD® notebook fresnelC(z) appears in a typeset notation as C(z).

For floating-point arguments, fresnelC returns floating-point values.

simplify and Simplify, fresnelC uses the reflection rule fresnelC(-z) = -fresnelC(z) to create a "normal form" of symbolic function calls. See 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

Call the Fresnel cosine integral function with various arguments:

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

For floating-point arguments, fresnelC returns floating-point values:

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

Example 2

diff, float, limit, series, and other functions handle expressions involving the Fresnel cosine integral function:

diff(fresnelC(x), x)

float(fresnelC(PI))

limit(fresnelC(x), x = infinity)

series(fresnelC(x), x = 0)

Example 3

simplify uses the reflection rule fresnelC(-z) = -fresnelC(z) to create a "normal form" of symbolic function calls:

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

Parameters

z

An arithmetical expression

Return Values

Arithmetical expression.

Overloaded By

z

See Also

MuPAD Functions

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