28.5 Functions and Variables for Fourier series

Function: equalp (x, y) ¶

Returns true if equal (x, y) otherwise false (doesn’t give an error message like equal (x, y) would do in this case).

‘Category: Package fourie’

Function: remfun
    remfun (f, expr)
    remfun (f, expr, x) ¶

remfun (f, expr) replaces all occurrences of f (arg) by arg in expr.

remfun (f, expr, x) replaces all occurrences of f (arg) by arg in expr only if arg contains the variable x.

‘Category: Package fourie’

Function: funp
    funp (f, expr)
    funp (f, expr, x) ¶

funp (f, expr) returns true if expr contains the function f.

funp (f, expr, x) returns true if expr contains the function f and the variable x is somewhere in the argument of one of the instances of f.

‘Category: Package fourie’

Function: absint
    absint (f, x, halfplane)
    absint (f, x)
    absint (f, x, a, b) ¶

absint (f, x, halfplane) returns the indefinite integral of f with respect to x in the given halfplane (pos, neg, or both). f may contain expressions of the form abs (x), abs (sin (x)), abs (a) * exp (-abs (b) * abs (x)).

absint (f, x) is equivalent to absint (f, x, pos).

absint (f, x, a, b) returns the definite integral of f with respect to x from a to b. f may include absolute values.

‘Category: Package fourie’ ‘Category: Integral calculus’

Function: fourier (f, x, p) ¶

Returns a list of the Fourier coefficients of f(x) defined on the interval [-p, p].

‘Category: Package fourie’

Function: foursimp (l) ¶

Simplifies sin (n %pi) to 0 if sinnpiflag is true and cos (n %pi) to (-1)^n if cosnpiflag is true.

‘Category: Package fourie’ ‘Category: Trigonometric functions’ ‘Category: Simplification functions’

Option variable: sinnpiflag ¶

Default value: true

See foursimp.

‘Category: Package fourie’

Option variable: cosnpiflag ¶

Default value: true

See foursimp.

‘Category: Package fourie’

Function: fourexpand (l, x, p, limit) ¶

Constructs and returns the Fourier series from the list of Fourier coefficients l up through limit terms (limit may be inf). x and p have same meaning as in fourier.

‘Category: Package fourie’

Function: fourcos (f, x, p) ¶

Returns the Fourier cosine coefficients for f(x) defined on [0, p].

‘Category: Package fourie’

Function: foursin (f, x, p) ¶

Returns the Fourier sine coefficients for f(x) defined on [0, p].

‘Category: Package fourie’

Function: totalfourier (f, x, p) ¶

Returns fourexpand (foursimp (fourier (f, x, p)), x, p, 'inf).

‘Category: Package fourie’

Function: fourint (f, x) ¶

Constructs and returns a list of the Fourier integral coefficients of f(x) defined on [minf, inf].

‘Category: Package fourie’

Function: fourintcos (f, x) ¶

Returns the Fourier cosine integral coefficients for f(x) on [0, inf].

‘Category: Package fourie’

Function: fourintsin (f, x) ¶

Returns the Fourier sine integral coefficients for f(x) on [0, inf].

‘Category: Package fourie’