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IntegrationTools

  

ExpandMultiple

  

expand a multiple integral into a nested integral

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ExpandMultiple(v)

ExpandMultiple(v, stripoptions)

Parameters

v

-

multiple integral

Description

• 

The function ExpandMultiple expands a multiple integral given as a single Int function call into a nested series of Int function calls.

• 

ExpandMultiple will also work similarly on unevaluated int function calls.

• 

This command is primarily intended for programmers who need to manipulate integrals as data structures.  In most cases, multiple integrals should be computed from a single function call.  The output of ExpandMultiple can be transformed back into a single function call using IntegrationTools[CollapseNested].

• 

If stripoptions is given, none of the options in the integral v will appear in the output

• 

If v is a nested Int or int function call, only the outermost function call will be expanded.

Examples

withIntegrationTools:

lprintIntfx,y,x,y

Int(f(x,y),[x, y])

ExpandMultipleIntfx,y,x,y

∫∫fx,yⅆxⅆy

(1)

lprint

Int(Int(f(x,y),x),y)

ExpandMultipleIntfx,y,x,y

∫∫fx,yⅆxⅆy

(2)

lprint

Int(Int(f(x,y),x),y)

ExpandMultiple∫cd∫abfx,yⅆxⅆy

∫cd∫abfx,yⅆxⅆy

(3)

lprint

Int(Int(f(x,y),x = a .. b),y = c .. d)

CollapseNested

∫cd∫abfx,yⅆxⅆy

(4)

lprint

Int(f(x,y),[x = a .. b, y = c .. d])

ExpandMultiple'int'fx,y,x=a..b,y=c..d

∫cd∫abfx,yⅆxⅆy

(5)

lprint

int(int(f(x,y),x = a .. b),y = c .. d)

ExpandMultipleIntfx,y,x=a..b,y=c..d,CauchyPrincipalValue

IntIntfx,y,x=a..b,CauchyPrincipalValue,y=c..d,CauchyPrincipalValue

(6)

lprint

Int(Int(f(x,y),x = a .. b,CauchyPrincipalValue),y = c .. d,CauchyPrincipalValue)

ExpandMultipleIntfx,y,x=a..b,y=c..d,CauchyPrincipalValue,stripoptions

∫cd∫abfx,yⅆxⅆy

(7)

lprint

Int(Int(f(x,y),x = a .. b),y = c .. d)

See Also

int

IntegrationTools

IntegrationTools[CollapseNested]

 


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