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FunctionAdvisor/display

display information about a mathematical function organized in sections

FunctionAdvisor/table

return a table of information about a mathematical function

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

FunctionAdvisor(math_function)

FunctionAdvisor(display, math_function)

FunctionAdvisor(table, math_function)

Parameters

display

-

(optional) literal name;'display', since Maple 2016 it can be ommited,

math_function

-

name of known mathematical function; see type/mathfunc

table

-

(optional) literal name;'table', since Maple 2016 it returns a table of information about math_function

Description

• 

The FunctionAdvisor(math_function) command returns the information regarding that function available to the system. The information that displays is organized in sections as shown in the examples.

• 

Although the mathematical information in the sections is all computable (for instance, you can right click a formula and explore it, or just copy and paste it to work with it), it is sometimes convenient to have this information directly presented in a form that is more suitable for further computations. For this purpose use the optional argument table, in which case the same information is presented now as a table where the indices are the topics and the entries are the corresponding information.

Examples

The information about a mathematical function organized in closed sections

FunctionAdvisorsin

sin

describe

sin=sine function

definition

sinz=12IⅇIz1ⅇIz

with no restrictions on z

classify function

trig

elementary

symmetries

sinz=sinz

sinz&conjugate0;=sinz&conjugate0;

periodicity

sin2πm+z=sinz

Andm::integer

sinπm+z=1msinz

Andm::integer

plot

singularities

sinz

z=∞+∞I

branch points

sinz

No branch points

branch cuts

sinz

No branch cuts

special values

sin16π=12

sin14π=122

sin13π=123

sin∞=undefined

sin∞I=∞I

sinπn=0

Andn::integer

sin122n+1π=1

Andn::odd

sin122n+1π=1

Andn::even

identities

sinarcsinz=z

sinz=sinz

sinz=2sin12zcos12z

sinz=1cscz

sinz=2tan12z1+tan12z2

sinz=12IⅇIzⅇIz

sinz2=1cosz2

sinz2=1212cos2z

sum form

sinz=_k1=0∞1_k1z2_k1+12_k1+1!

with no restrictions on z

series

seriessinz,z,4=z16z3+Oz5

integral form

sinz=z∫01ⅇ2I_t1zⅆ_t1ⅇIz

with no restrictions on z

differentiation rule

ⅆⅆzsinz=cosz

ⅆnⅆznsinz=sinz+12nπ

DE

fz=sinz

ⅆⅆzⅆⅆzfz=fz

To get a Maple table structure with this same information use the table keyword (to avoid verbosity, use the option quiet)

sin_infoFunctionAdvisortable,sin,quiet

sin_infotableseries=seriessinz,z,4=z16z3+Oz5,classify_function=trig,elementary,branch_points=sinz,No branch points,symmetries=sinz=sinz,sinz&conjugate0;=sinz&conjugate0;,describe=sin=sine function,calling_sequence=sinz,DE=fz=sinz,ⅆ2ⅆz2fz=fz,asymptotic_expansion=,sum_form=sinz=_k1=0∞1_k1z2_k1+12_k1+1!,with no restrictions on z,definition=sinz=12IⅇIz1ⅇIz,with no restrictions on z,special_values=sin16π=12,sin14π=122,sin13π=123,sin∞=undefined,sin∞I=∞I,sinπn=0,Andn::integer,sin122n+1π=1,Andn::odd,sin122n+1π=1,Andn::even,identities=sinarcsinz=z,sinz=sinz,sinz=2sin12zcos12z,sinz=1cscz,sinz=2tan12z1+tan12z2,sinz=12IⅇIzⅇIz,sinz2=1cosz2,sinz2=1212cos2z,periodicity=sin2πm+z=sinz,Andm::integer,sinπm+z=1msinz,Andm::integer,singularities=sinz,z=∞+∞I,integral_form=sinz=z∫01ⅇ2I_t1zⅆ_t1ⅇIz,with no restrictions on z,differentiation_rule=ⅆⅆzsinz=cosz,ⅆnⅆznsinz=sinz+12nπ,branch_cuts=sinz,No branch cuts

(1)

You can now access the information indexing with the FunctionAdvisor topics

sin_infodifferentiation_rule

ⅆⅆzsinz=cosz,ⅆnⅆznsinz=sinz+12nπ

(2)

Compatibility

• 

The FunctionAdvisor/table command was introduced in Maple 2016.

• 

For more information on Maple 2016 changes, see Updates in Maple 2016.

See Also

entries

FunctionAdvisor

FunctionAdvisor/topics

indices

table

type/mathfunc

 


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