`fresnelc`

Fresnel cosine integral.

Category: Mathematics > Mathematical Functions

Syntax

C = fresnelc(X)

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

Description

Together with fresnels it describes the Euler (Cornu) spiral, the curve (C(t), S(t)), and appears in diffraction at a straight edge and in the design of transition curves in roads and railways. This definition uses the pi/2 scaling in the argument; other texts omit it.

Input arguments

X: Numeric or symbolic array.

Output arguments

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

Example

Values and the limit

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

Output

ans = 1×3

         0    0.4923    0.7799
ans = 0.5000

See also

fresnels erf erfi cosint