Evaluate numerically to high precision:

Precision of the output tracks the precision of the input:

Evaluate for complex argument:

Evaluate FresnelG 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 FresnelG function using MatrixFunction:

Value at a fixed point:

Values at infinity:

Find a local maximum as a root of :

Plot the FresnelG function:

Plot the real part of :

Plot the imaginary part of :

FresnelG is defined for all real and complex values:

Approximate function range of FresnelG:

FresnelG is an analytic function of x:

FresnelG is monotonic in a specific range:

FresnelG is not injective:

FresnelG is not surjective:

FresnelG is neither non-negative nor non-positive:

FresnelG has no singularities or discontinuities:

Neither convex nor concave:

First derivative:

Higher derivatives:

Indefinite integral of FresnelG:

More integrals:

Approximation of the definite integral of FresnelG:

Taylor expansion for FresnelG:

Plot the first three approximations for FresnelG around :

Taylor expansion for FresnelG at a generic point:

Find series expansion at infinity:

Give the result for an arbitrary symbolic direction :

Primary definition:

Argument simplifications:

FresnelG threads elementwise over lists and matrices:

TraditionalForm typesetting: