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Calling Sequence
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addtable(tname, patt, expr, t, s, parameter, condition, additional)
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Parameters
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tname
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name of transform for which patt is to be added to the lookup table
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patt
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pattern to be added to table
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expr
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transform of patt
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t
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independent variable in patt
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s
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independent variable in expr
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parameter
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(optional) list or set of parameters in patt and expr
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condition
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(optional) conditions that the parameters must satisfy
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additional
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additional argument for hankel and invmellin tables. This parameter is required for hankel and invmellin transform
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Description
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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.
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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.
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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.
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The hankel and invmellin transforms take additional arguments in the transform. For this reason, they also take additional arguments within the <addtable>.
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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.
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The format for invmellin is of the form , to specify that the transform can only be performed if the additional argument is contained within the range 3 to 5.
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Examples
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| (1) |
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addtable(fourier,f(t),F(s),t,s);
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Functions with parameters
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addtable(
laplace,g(x*a+b),G(s+a)/(b-a),x,s,{a,b}):
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Functions with conditional parameters
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addtable(hilbert,f(a,t),F(s-a),t,s,{a},a::Range(3,7)):
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| (7) |
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addtable(mellin, h(a,t), F(s-a),t,s,{a},_evalb(a=Pi));
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Hankel and invmellin transform
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addtable(hankel,f(t),F(s,mu),t,s,hankel=mu::Range(-infinity,infinity)):
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addtable(hankel,g(t*a),G(s-a,mu),t,s,{a},hankel=mu::Range(-3,3)):
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| (13) |
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invmellin(f(t),t,s,1..2);
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| (15) |
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addtable(invmellin,f(t*a),F(t-a),t,s,{a},a::Range(-3,3),invmellin=0..3):
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invmellin(f(t),t,s,1..2);
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