`fresnels`

Fresnel sine integral.

Category: Mathematics > Mathematical Functions

Syntax

S = fresnels(X)

Evaluates the integral from 0 to x of sin(pi*t^2/2).

Description

fresnels is the companion of fresnelc. Both oscillate around 0.5 for large x with decreasing amplitude, which makes the Euler spiral wind toward the point (0.5, 0.5). Near the origin S(x) behaves like pi*x^3/6.

Input arguments

X: Numeric or symbolic array.

Output arguments

S: Array of the same size; odd in x, with limit 0.5 as x goes to Inf.

Example

Values and the limit

fresnels([0 0.5 1])
fresnels(Inf)

Output

ans = 1×3

         0    0.0647    0.4383
ans = 0.5000

See also

fresnelc erf sinint erfi