FunctionAdvisor/integral_form - Maple Programming Help

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FunctionAdvisor/integral_form

return the integral form of a given mathematical function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

FunctionAdvisor(integral_form, math_function)

Parameters

integral_form

-

literal name; 'integral_form'

math_function

-

Maple name of mathematical function

Description

• 

The FunctionAdvisor(integral_form, math_function) command returns the integral form for the function, if it exists.

Examples

FunctionAdvisorintegral_form,sin

sinz=z01ⅇ2I_t1zⅆ_t1ⅇIz,with no restrictions on z

(1)

FunctionAdvisorintegral_form,Βa,z

Βa&comma;z=01_k1a11_k1z1&DifferentialD;_k1&comma;0<a0<z

(2)

FunctionAdvisordescribe&comma;EllipticE

EllipticE=incomplete or complete elliptic integral of the second kind

(3)

FunctionAdvisorintegral&comma;EllipticE

* Partial match of "integral" against topic "integral_form".

EllipticEk=01k2_&alpha;12+1_&alpha;12+1&DifferentialD;_&alpha;1&comma;with no restrictions on k,EllipticEz&comma;k=0zk2_&alpha;12+1_&alpha;12+1&DifferentialD;_&alpha;1&comma;with no restrictions on z&comma;k

(4)

ex1FunctionAdvisorintegral&comma;BesselJ

* Partial match of "integral" against topic "integral_form".

ex1BesselJa&comma;z=ππ12π&ExponentialE;Ia_k1Izsin_k1&DifferentialD;_k1&comma;a::?,BesselJa&comma;z=02sinzcosh_k1+πa2cosha_k1π&DifferentialD;_k1&comma;z::real,BesselJa&comma;z=0πcosa_k1zsin_k1π&DifferentialD;_k1sinπa01&ExponentialE;I_k1+zsinh_k1&DifferentialD;_k1π&comma;0<z,BesselJa&comma;z=za01&ExponentialE;2I_t1z_t112+a1_t112+a&DifferentialD;_t121+2a22aΓ12+a&ExponentialE;Izπ&comma;0<12+a

(5)

The variables used by the FunctionAdvisor command to create the function calling sequences are local variables. Therefore, the previous example does not depend on a or z.

dependsex1&comma;a&comma;dependsex1&comma;z

false,false

(6)

To make the FunctionAdvisor command return resulting using global variables, pass the function call itself.

FunctionAdvisorcalling&comma;EllipticF

* Partial match of "calling" against topic "calling_sequence".

EllipticFz&comma;k

(7)

ex2FunctionAdvisorintegral&comma;EllipticFa&comma;z

* Partial match of "integral" against topic "integral_form".

ex2EllipticFa&comma;z=0a1_&alpha;12+1z2_&alpha;12+1&DifferentialD;_&alpha;1&comma;with no restrictions on a&comma;z

(8)

dependsex2&comma;a&comma;dependsex2&comma;z

true,true

(9)

See Also

depends

FunctionAdvisor

FunctionAdvisor/definition

FunctionAdvisor/sum_form

FunctionAdvisor/topics