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# FresnelS

 FresnelS[z]gives the Fresnel integral .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• FresnelS[z] is an entire function of z with no branch cut discontinuities.
• For certain special arguments, FresnelS automatically evaluates to exact values.
• FresnelS can be evaluated to arbitrary numerical precision.
• FresnelS automatically threads over lists.
Evaluate numerically:
 Scope   (7)
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Simple exact values are generated automatically:
Parity transformation is automatically applied:
FresnelS threads element-wise over lists:
TraditionalForm formatting:
FresnelS can be applied to power series:
Find series expansions at infinity:
Give the result for an arbitrary symbolic direction :
 Applications   (4)
Intensity of a wave diffracted by a half-plane:
Plot a Cornu spiral:
A solution of the time-dependent 1D Schrödinger equation for a sudden opening of a shutter:
Check the Schrödinger equation:
Plot the time-dependent solution:
Plot of FresnelS along a circle in the complex plane:
Use FullSimplify to simplify expressions containing Fresnel integrals:
Find a numerical root:
Obtain FresnelS from integrals and sums:
Solve a differential equation:
Calculate the Wronskian:
Compare with Wronskian:
Integrals:
Integral transforms:
FresnelS can take large values for moderate-size arguments:
Nested integrals:
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