inttrans

 add entry to transform lookup table

Parameters

 tname - name of transform for which patt is to be added to the lookup table patt - pattern to be added to table expr - transform of patt t - independent variable in patt s - independent variable in expr parameter - (optional) list or set of parameters in patt and expr condition - (optional) conditions that the parameters must satisfy additional - additional argument for hankel and invmellin tables. This parameter is required for hankel and invmellin transform

Description

 • Adds an entry to the lookup table for the integral transform . After this function is executed, any call to with argument will result in 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 may include any number of parameters, which may also be used in the transform expression .  Conditions may be placed on the parameters, by using the argument. The 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 .
 • 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.

Examples

 > with(inttrans):
 > fourier(f(t),t,s);
 ${ℱ}{}\left({f}{}\left({t}\right){,}{t}{,}{s}\right)$ (1)
 > fourier(f(x),x,z);
 ${F}{}\left({z}\right)$ (2)

Functions with parameters

 > laplace(g(p*a+b),p,x);
  (3)
 > laplace(g(-p),p,x);
 ${G}{}\left({x}{-}{1}\right)$ (4)
 > laplace(g(3*p+2),p,x);
 ${-}{G}{}\left({x}{+}{3}\right)$ (5)

Functions with conditional parameters

 > hilbert(f(a*t),t,s);
 ${ℍ}{}\left({f}{}\left({a}{}{t}\right){,}{t}{,}{s}\right)$ (6)
 > hilbert(f(a,t),t,s);
 ${ℍ}{}\left({f}{}\left({a}{,}{t}\right){,}{t}{,}{s}\right)$ (7)
 > assume(a>3,a<7):
 > hilbert(f(a,t),t,s);
 ${F}{}\left({s}{-}{\mathrm{a~}}\right)$ (8)
 > mellin(h(a,x),x,s);
 ${ℳ}{}\left({h}{}\left({\mathrm{a~}}{,}{x}\right){,}{x}{,}{s}\right)$ (9)
 > mellin(h(Pi,x),x,s);
 ${F}{}\left({s}{-}{\mathrm{\pi }}\right)$ (10)

Hankel and invmellin transform

 > hankel(f(t),t,s,nu);
 ${ℋ}{}\left({f}{}\left({t}\right){,}{t}{,}{s}{,}{\mathrm{ν}}\right)$ (11)
 > hankel(f(t),t,s,nu);
 ${F}{}\left({s}{,}{\mathrm{\nu }}\right)$ (12)
 > hankel(g(2*t),t,s,nu);
 ${ℋ}{}\left({g}{}\left({2}{}{t}\right){,}{t}{,}{s}{,}{\mathrm{ν}}\right)$ (13)
 > assume(1
 > hankel(g(2*t),t,s,nu);
 ${G}{}\left({s}{-}{2}{,}{\mathrm{ν~}}\right)$ (14)
 > invmellin(f(t),t,s,1..2);
 ${\mathrm{invmellin}}{}\left({f}{}\left({t}\right){,}{t}{,}{s}{,}{1}{..}{2}\right)$ (15)
 ${F}{}\left({t}{-}{1}\right)$ (16)