### 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).

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  Categories: 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.

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  Categories: 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.

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  Categories: 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.

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  Categories: Package fourie ·Integral calculus

Function: fourier (f, x, p)

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

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  Categories: 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`.

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  Categories: Package fourie ·Trigonometric functions ·Simplification functions

Option variable: sinnpiflag

  Default value: `true`

  See `foursimp`.

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  Categories: Package fourie

Option variable: cosnpiflag

  Default value: `true`

  See `foursimp`.

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  Categories: 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`.

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  Categories: Package fourie

Function: fourcos (f, x, p)

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

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  Categories: Package fourie

Function: foursin (f, x, p)

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

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  Categories: Package fourie

Function: totalfourier (f, x, p)

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

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  Categories: Package fourie

Function: fourint (f, x)

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

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  Categories: Package fourie

Function: fourintcos (f, x)

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

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  Categories: Package fourie

Function: fourintsin (f, x)

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

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  Categories: Package fourie