return the differentiation rule of a given mathematical function - Maple Help

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FunctionAdvisor/differentiation_rule - return the differentiation rule of a given mathematical function

Calling Sequence

FunctionAdvisor(differentiation_rule, math_function)

Parameters

differentiation_rule

-

literal name; 'differentiation_rule'

math_function

-

Maple name of mathematical function

Description

• 

The FunctionAdvisor(differentiation_rule, math_function) command returns the differentiation rule for the function.

Examples

FunctionAdvisordifferentiation_rule,arcsin

ⅆⅆzarcsinz=1z2+1

(1)

FunctionAdvisordifferentiation_rule,dilog

ⅆⅆzdilogz=lnz1z

(2)

The variables used by the FunctionAdvisor command to create the calling sequence are local variables. To make the FunctionAdvisor command return results using global variables, pass the actual function call instead of the function name.  Compare the following two input and output groups.

eq1:=FunctionAdvisordiff,ζ

* Partial match of "diff" against topic "differentiation_rule".

eq1:=sζn,s,a=ζn+1,s,a,aζn,s,a=sζn,s+1,a{0n=0nζn1,s+1,aotherwise

(3)

haseq1,a,haseq1,b,haseq1,z

false,false,false

(4)

eq2:=FunctionAdvisordiff,ζa,b,z

* Partial match of "diff" against topic "differentiation_rule".

eq2:=bζa,b,z=ζa+1,b,z,zζa,b,z=bζa,b+1,z{0a=0aζa1,b+1,zotherwise

(5)

haseq2,a,haseq2,b,haseq2,z

true,true,true

(6)

For functions which accept different numbers of parameters, you can specify for which function call you want the differentiation rule by specifying the function with the appropriate number of arguments. For example, for Zeta, if given with only one argument specified, it represents the Hurwitz Zeta function and its differentiation rule is the following.

FunctionAdvisordiff,ζz

* Partial match of "diff" against topic "differentiation_rule".

ⅆⅆzζz=ζ1,z

(7)

FunctionAdvisordifferentiation_rule,Eiz

ⅆⅆzEiz=ⅇzz

(8)

FunctionAdvisordifferentiation_rule,Eia,z

aEia,z=zaMeijerG,0,0,1,1,a,,z,zEia,z=Eia1,z

(9)

As another example, consider the exponential integral Ei.

FunctionAdvisordifferentiation_rule,Eiz

ⅆⅆzEiz=ⅇzz

(10)

FunctionAdvisordifferentiation_rule,Eia,z

aEia,z=zaMeijerG,0,0,1,1,a,,z,zEia,z=Eia1,z

(11)

See Also

Ei, FunctionAdvisor, FunctionAdvisor/DE, FunctionAdvisor/topics, Zeta


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