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=z∫01ⅇ2I_t1zⅆ_t1ⅇIz,MathematicalFunctions:-with no restrictions on z

(1)

FunctionAdvisorintegral_form,Βa,z

&Beta;a&comma;z&equals;&int;01_k1a11_k1z1&DifferentialD;_k1&comma;And0<&real;a&comma;0<&real;z

(2)

FunctionAdvisordescribe&comma;EllipticE

EllipticE&equals;incomplete or complete elliptic integral of the second kind

(3)

FunctionAdvisorintegral&comma;EllipticE

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

EllipticEk&equals;&int;01_&alpha;12k2&plus;1_&alpha;12&plus;1&DifferentialD;_&alpha;1&comma;MathematicalFunctions:-with no restrictions on k&comma;EllipticEz&comma;k&equals;&int;0z_&alpha;12k2&plus;1_&alpha;12&plus;1&DifferentialD;_&alpha;1&comma;MathematicalFunctions:-with no restrictions on z&comma;k

(4)

ex1FunctionAdvisorintegral&comma;BesselJ

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

ex1:=BesselJa&comma;z&equals;&int;&pi;&pi;12&pi;&ExponentialE;Ia_k1Izsin_k1&DifferentialD;_k1&comma;Anda::integer&comma;BesselJa&comma;z&equals;&int;0&infin;2sinzcosh_k1&plus;12&pi;acosha_k1&pi;&DifferentialD;_k1&comma;Andz::real&comma;BesselJa&comma;z&equals;&int;0&pi;cosa_k1zsin_k1&pi;&DifferentialD;_k1sin&pi;a&int;0&infin;1&ExponentialE;I_k1&plus;zsinh_k1&DifferentialD;_k1&pi;&comma;And0<&real;z&comma;BesselJa&comma;z&equals;12za&int;01&ExponentialE;2I_t1z_t112&plus;a1_t112&plus;a&DifferentialD;_t121&plus;2a2a&Gamma;12&plus;a&ExponentialE;Iz&pi;&comma;And0<12&plus;&real;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&comma;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".

ex2:=EllipticFa&comma;z&equals;&int;0a1_&alpha;12&plus;1_&alpha;12z2&plus;1&DifferentialD;_&alpha;1&comma;MathematicalFunctions:-with no restrictions on a&comma;z

(8)

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

true&comma;true

(9)

See Also

depends

FunctionAdvisor

FunctionAdvisor/definition

FunctionAdvisor/sum_form

FunctionAdvisor/topics

 


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