(maxima.info)Functions and Variables for Fourier series

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28.5 Functions and Variables for Fourier series
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 -- 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).

 -- 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>.

 -- 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>.

 -- 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.

 -- Function: fourier (<f>, <x>, <p>)

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

 -- Function: foursimp (<l>)

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

 -- Option variable: sinnpiflag
     Default value: 'true'

     See 'foursimp'.

 -- Option variable: cosnpiflag
     Default value: 'true'

     See 'foursimp'.

 -- 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'.

 -- Function: fourcos (<f>, <x>, <p>)

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

 -- Function: foursin (<f>, <x>, <p>)

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

 -- Function: totalfourier (<f>, <x>, <p>)

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

 -- Function: fourint (<f>, <x>)

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

 -- Function: fourintcos (<f>, <x>)

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

 -- Function: fourintsin (<f>, <x>)

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