gives the Fresnel auxiliary function .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- FresnelG[z] is an entire function of z with no branch cut discontinuities.
- For certain special arguments, FresnelG automatically evaluates to exact values.
- FresnelG can be evaluated to arbitrary numerical precision.
- FresnelG automatically threads over lists.
Examplesopen allclose all
Basic Examples (4)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Numerical Evaluation (3)
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:
Specific Values (3)
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 :
Differentiation and Integration (3)
Approximation of the definite integral of FresnelG:
Series Expansions (2)
Taylor expansion for FresnelG:
Plot the first three approximations for FresnelG around :
Taylor expansion for FresnelG at a generic point:
Function Identities and Simplifications (2)
Interference pattern at the edge of a shadow:
Introduced in 2014