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convert/Chebyshev - convert special functions admitting 2F1 hypergeometric representation into Chebyshev functions
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Calling Sequence
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convert(expr, Chebyshev)
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Parameters
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expr
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Maple expression, equation, or a set or list of them
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Description
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convert/Chebyshev converts, when possible, special functions admitting a 2F1 hypergeometric representation into Chebyshev functions (see ?ChebyshevT and ?ChebyshevU). The Chebyshev functions are
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FunctionAdvisor( Chebyshev );
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The 2 functions in the "Chebyshev" class are:
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![[ChebyshevT, ChebyshevU]](/support/helpjp/helpview.aspx?si=7078/file03598/math52.png)
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Examples
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![(a+1)*hypergeom([-a, a+2], [3/2], 1/2-(1/2)*z)](/support/helpjp/helpview.aspx?si=7078/file03598/math60.png)
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![(a+1)*hypergeom([-a, a+2], [3/2], 1/2-(1/2)*z)](/support/helpjp/helpview.aspx?si=7078/file03598/math63.png)
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![convert((a+1)*hypergeom([-a, a+2], [3/2], 1/2-(1/2)*z), Chebyshev)](/support/helpjp/helpview.aspx?si=7078/file03598/math67.png)
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![-sin(Pi*a)*a*MeijerG([[1-a, a+1], []], [[0], [1/2]], -1/2+(1/2)*z)/Pi^(1/2)](/support/helpjp/helpview.aspx?si=7078/file03598/math88.png)
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![-sin(Pi*a)*a*MeijerG([[1-a, a+1], []], [[0], [1/2]], -1/2+(1/2)*z)/Pi^(1/2)](/support/helpjp/helpview.aspx?si=7078/file03598/math91.png)
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![simplify(convert(-sin(Pi*a)*a*MeijerG([[1-a, a+1], []], [[0], [1/2]], -1/2+(1/2)*z)/Pi^(1/2), Chebyshev))](/support/helpjp/helpview.aspx?si=7078/file03598/math95.png)
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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:
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Download Help Document
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