Adds an entry to the lookup table for the integral transform <tname>. After this function is executed, any call to <tname> with argument <patt> will result in <expr> being returned.

If you wish this information to be saved across sessions, a facility exists, savetable, that will save the information of a particular table to a particular file.

The expression <patt> may include any number of parameters, which may also be used in the transform expression <expr>.  Conditions may be placed on the parameters, by using the <conditional> argument. The <conditional> statement must be an unevaluated operator which evaluates to type boolean.  Unevaluated operators include Range, _testeq, _signum, and _evalb.

The hankel and invmellin transforms take additional arguments in the transform.  For this reason, they also take additional arguments within the <addtable>.

The format for hankel is of the form hankel=mu::Range(-1,infinity), to specify that the transform can be performed only if the additional argument to hankel is within the range -1 to infinity.

The format for invmellin is of the form $\mathrm{invmellin}=3..5$, to specify that the transform can only be performed if the additional argument is contained within the range 3 to 5.

with(inttrans):

fourier(f(t),t,s);

$ℱ\left(f\left(t\right)\&comma;t\&comma;s\right)$

addtable(fourier,f(t),F(s),t,s);

fourier(f(x),x,z);

$F\left(z\right)$

laplace(g(p*a+b),p,x);

addtable(
  laplace,g(x*a+b),G(s+a)/(b-a),x,s,{a,b}):

laplace(g(-p),p,x);

$G\left(x-1\right)$

laplace(g(3*p+2),p,x);

$-G\left(x+3\right)$

hilbert(f(a*t),t,s);

$ℍ\left(f\left(at\right)\&comma;t\&comma;s\right)$

addtable(hilbert,f(a,t),F(s-a),t,s,{a},a::Range(3,7)):

hilbert(f(a,t),t,s);

$ℍ\left(f\left(a\&comma;t\right)\&comma;t\&comma;s\right)$

assume(a>3,a<7):

hilbert(f(a,t),t,s);

$F\left(s-\mathrm{a~}\right)$

addtable(mellin, h(a,t), F(s-a),t,s,{a},_evalb(a=Pi));

mellin(h(a,x),x,s);

$ℳ\left(h\left(\mathrm{a~}\&comma;x\right)\&comma;x\&comma;s\right)$

mellin(h(Pi,x),x,s);

$F\left(s-\mathrm{\pi }\right)$

hankel(f(t),t,s,nu);

$\mathscr{H}\left(f\left(t\right)\&comma;t\&comma;s\&comma;\mathrm{\&nu;}\right)$

addtable(hankel,f(t),F(s,mu),t,s,hankel=mu::Range(-infinity,infinity)):

hankel(f(t),t,s,nu);

$F\left(s\&comma;\mathrm{\nu }\right)$

addtable(hankel,g(t*a),G(s-a,mu),t,s,{a},hankel=mu::Range(-3,3)):

hankel(g(2*t),t,s,nu);

$\mathscr{H}\left(g\left(2t\right)\&comma;t\&comma;s\&comma;\mathrm{\&nu;}\right)$

assume(1<nu,nu<2):

hankel(g(2*t),t,s,nu);

$G\left(s-2\&comma;\mathrm{\&nu;~}\right)$

invmellin(f(t),t,s,1..2);

$\mathrm{invmellin}\left(f\left(t\right)\&comma;t\&comma;s\&comma;1..2\right)$

addtable(invmellin,f(t*a),F(t-a),t,s,{a},a::Range(-3,3),invmellin=0..3):

invmellin(f(t),t,s,1..2);

$F\left(t-1\right)$