convert/Chebyshev
convert special functions admitting 2F1 hypergeometric representation into Chebyshev functions
Calling Sequence
Parameters
Description
Examples
convert(expr, Chebyshev)
expr
-
Maple expression, equation, or a set or list of them
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
a+1hypergeom−a,a+2,32,12−12z
a+1hypergeom−a,a+2,32,12−z2
convert,Chebyshev
ChebyshevUa,z
JacobiP−a+b,−12,−12,12z+JacobiPa−b,12,12,12z
JacobiP−a+b,−12,−12,z2+JacobiPa−b,12,12,z2
−a+b−12−12ChebyshevTa−b,z2+a−b+1212ChebyshevUa−b,z2a−b+1
−1π12sinπaaMeijerG1−a,a+1,,0,12,−12+12z
−sinπaaMeijerG1−a,a+1,,0,12,−12+z2π
simplifyconvert,Chebyshev
ChebyshevTa,z
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
convert,Chebyshev,raise a
ChebyshevU−4−a,z−2zChebyshevU−3−a,z
See Also
convert
convert/to_special_function
FunctionAdvisor
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