Evaluate numerically to high precision:

The precision of the output tracks the precision of the input:

Evaluate for complex arguments:

Evaluate FresnelC efficiently at high precision:

Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:

Or compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix FresnelC function using MatrixFunction:

Value at a fixed point:

Values at infinity:

Find a local maximum as a root of :

Plot the FresnelC function:

Plot the real part of :

Plot the imaginary part of :

FresnelC is defined for all real and complex values:

Approximate function range of FresnelC:

FresnelC is an odd function:

FresnelC is an analytic function of x:

FresnelC is neither non-increasing nor non-decreasing:

FresnelC is not injective:

FresnelC is not surjective:

FresnelC is neither non-negative nor non-positive:

FresnelC has no singularities or discontinuities:

Neither convex nor concave:

First derivative:

Higher derivatives:

Formula for the derivative:

Indefinite integral of FresnelC:

Definite integral of an odd integrand over an interval centered at the origin is 0:

More integrals:

Taylor expansion for FresnelC:

Plot the first three approximations for FresnelC around :

General term in the series expansion of FresnelC:

Find series expansion at infinity:

Give the result for an arbitrary symbolic direction :

FresnelC can be applied to power series:

Compute the Laplace transform using LaplaceTransform:

MellinTransform:

Verify an identity relating HypergeometricPFQ to FresnelC:

Simplify an integral to FresnelC:

Argument simplifications:

Integral representation:

Relation to the error function Erf:

FresnelC can be represented as a DifferentialRoot:

FresnelC can be represented in terms of MeijerG:

TraditionalForm formatting: