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inttrans

  

addtable

  

add entry to transform lookup table

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

addtable(tname, patt, expr, t, s, parameter, condition, additional)

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 <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 invmellin&equals;3..5, to specify that the transform can only be performed if the additional argument is contained within the range 3 to 5.

Examples

withinttrans&colon;

fourierft&comma;t&comma;s

fourierft&comma;t&comma;s

(1)

addtablefourier&comma;ft&comma;Fs&comma;t&comma;s

fourierfx&comma;x&comma;z

Fz

(2)

Functions with parameters

laplacegpa&plus;b&comma;p&comma;x

laplacegap&plus;b&comma;p&comma;x

(3)

addtablelaplace&comma;gxa&plus;b&comma;Gs&plus;aba&comma;x&comma;s&comma;a&comma;b&colon;

laplacegp&comma;p&comma;x

Gx1

(4)

laplaceg3p&plus;2&comma;p&comma;x

Gx&plus;3

(5)

Functions with conditional parameters

hilbertfat&comma;t&comma;s

hilbertfat&comma;t&comma;s

(6)

addtablehilbert&comma;fa&comma;t&comma;Fsa&comma;t&comma;s&comma;a&comma;a::Range3&comma;7&colon;

hilbertfa&comma;t&comma;t&comma;s

hilbertfa&comma;t&comma;t&comma;s

(7)

assume3<a&comma;a<7&colon;

hilbertfa&comma;t&comma;t&comma;s

Fsa~

(8)

addtablemellin&comma;ha&comma;t&comma;Fsa&comma;t&comma;s&comma;a&comma;_evalba&equals;&pi;

mellinha&comma;x&comma;x&comma;s

mellinha~&comma;x&comma;x&comma;s

(9)

mellinh&pi;&comma;x&comma;x&comma;s

Fs&pi;

(10)

Hankel and invmellin transform

hankelft&comma;t&comma;s&comma;&nu;

hankelft&comma;t&comma;s&comma;&nu;

(11)

addtablehankel&comma;ft&comma;Fs&comma;&mu;&comma;t&comma;s&comma;hankel&equals;&mu;::Range&infin;&comma;&infin;&colon;

hankelft&comma;t&comma;s&comma;&nu;

Fs&comma;&nu;

(12)

addtablehankel&comma;gta&comma;Gsa&comma;&mu;&comma;t&comma;s&comma;a&comma;hankel&equals;&mu;::Range3&comma;3&colon;

hankelg2t&comma;t&comma;s&comma;&nu;

hankelg2t&comma;t&comma;s&comma;&nu;

(13)

assume1<&nu;&comma;&nu;<2&colon;

hankelg2t&comma;t&comma;s&comma;&nu;

Gs2&comma;&nu;~

(14)

invmellinft&comma;t&comma;s&comma;1..2

invmellinft&comma;t&comma;s&comma;1..2

(15)

addtableinvmellin&comma;fta&comma;Fta&comma;t&comma;s&comma;a&comma;a::Range3&comma;3&comma;invmellin&equals;0..3&colon;

invmellinft&comma;t&comma;s&comma;1..2

Ft1

(16)

See Also

insertpattern

inttrans

inttrans[savetable]

patmatch

 


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