convert/Chebyshev - Maple Programming Help

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convert/Chebyshev

convert special functions admitting 2F1 hypergeometric representation into Chebyshev functions

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

convert(expr, Chebyshev)

Parameters

expr

-

Maple expression, equation, or a set or list of them

Description

• 

convert/Chebyshev converts, when possible, special functions admitting a 2F1 hypergeometric representation into Chebyshev functions (see ?ChebyshevT and ?ChebyshevU). The Chebyshev functions are

FunctionAdvisor( Chebyshev );

The 2 functions in the "Chebyshev" class are:

ChebyshevT,ChebyshevU

(1)

Examples

a+1hypergeoma,a+2,32,121z2

a+1hypergeoma,a+2,32,1212z

(2)

convert,Chebyshev

ChebyshevUa,z

(3)

JacobiPa+b,12,12,1z2+JacobiPab,12,12,1z2

JacobiPa+b,12,12,12z+JacobiPab,12,12,12z

(4)

convert,Chebyshev

binomial12a+b,12ChebyshevTab,12z+binomial12+ab,12ChebyshevUab,12zab+1

(5)

1sinπaaMeijerG1a,a+1,,0,12,12+1z2π12

sinπaaMeijerG1a,a+1,,0,12,12+12zπ

(6)

simplifyconvert,Chebyshev

ChebyshevTa,z

(7)

When converting to a function class (e.g. Chebyshev) it is possible to request additional conversion rules to be performed. Compare for instance these two different outputs:

GegenbauerCa,1,z

GegenbauerCa,1,z

(8)

convert,Chebyshev

ChebyshevUa,z

(9)

convert,Chebyshev,raise a

ChebyshevU4a,z2zChebyshevU3a,z

(10)

See Also

convert

convert/to_special_function

FunctionAdvisor

 


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