FunctionAdvisor/integral_form
return the integral form of a given mathematical function
Calling Sequence
Parameters
Description
Examples
FunctionAdvisor(integral_form, math_function)
integral_form
-
literal name; 'integral_form'
math_function
Maple name of mathematical function
The FunctionAdvisor(integral_form, math_function) command returns the integral form for the function, if it exists.
FunctionAdvisorintegral_form,sin
sinz=z∫01ⅇ2I_t1zⅆ_t1ⅇIz,with no restrictions on z
FunctionAdvisorintegral_form,Βa,z
Βa,z=∫01_k1a−11−_k1z−1ⅆ_k1,0<ℜa∧0<ℜz
FunctionAdvisordescribe,EllipticE
EllipticE=incomplete or complete elliptic integral of the second kind
FunctionAdvisorintegral,EllipticE
* Partial match of "integral" against topic "integral_form".
EllipticEk=∫01−k2_α12+1−_α12+1ⅆ_α1,with no restrictions on k,EllipticEz,k=∫0z−_α12k2+1−_α12+1ⅆ_α1,with no restrictions on z,k
ex1≔FunctionAdvisorintegral,BesselJ
ex1≔BesselJa,z=∫−ππ12πⅇIa_k1−zsin_k1ⅆ_k1,a::ℤ,BesselJa,z=∫0∞−2sin−zcosh_k1+aπ2cosha_k1πⅆ_k1,z::real,BesselJa,z=∫0πcosa_k1−zsin_k1πⅆ_k1−sinaπ∫0∞1ⅇI_k1+zsinh_k1ⅆ_k1π,0<ℜz,BesselJa,z=za∫01ⅇ2I_t1z_t1−12+a1−_t1−12+aⅆ_t121+2a22aΓ12+aⅇIzπ,0<12+ℜa
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,a,dependsex1,z
false,false
To make the FunctionAdvisor command return resulting using global variables, pass the function call itself.
FunctionAdvisorcalling,EllipticF
* Partial match of "calling" against topic "calling_sequence".
EllipticFz,k
ex2≔FunctionAdvisorintegral,EllipticFa,z
ex2≔EllipticFa,z=∫0a1−_α12+1−z2_α12+1ⅆ_α1,with no restrictions on a,z
dependsex2,a,dependsex2,z
true,true
See Also
depends
FunctionAdvisor
FunctionAdvisor/definition
FunctionAdvisor/sum_form
FunctionAdvisor/topics
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