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convert/Legendre - convert special functions admitting 2F1 hypergeometric representation into Legendre functions
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Calling Sequence
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convert(expr, Legendre)
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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/Legendre converts, when possible, special functions admitting a 2F1 hypergeometric representation into Legendre functions. The Legendre functions are
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FunctionAdvisor( Legendre );
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The 2 functions in the "Legendre" class are:
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![[LegendreP, LegendreQ]](/support/helpjp/helpview.aspx?si=7087/file03612/math49.png)
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Examples
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![MeijerG([[-(1/2)*a-(1/2)*b, 1/2-(1/2)*a-(1/2)*b], []], [[0], [-1/2-a]], -1/z^2)](/support/helpjp/helpview.aspx?si=7087/file03612/math85.png)
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![MeijerG([[-(1/2)*a-(1/2)*b, 1/2-(1/2)*a-(1/2)*b], []], [[0], [-1/2-a]], -1/z^2)](/support/helpjp/helpview.aspx?si=7087/file03612/math88.png)
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![convert(MeijerG([[-(1/2)*a-(1/2)*b, 1/2-(1/2)*a-(1/2)*b], []], [[0], [-1/2-a]], -1/z^2), Legendre)](/support/helpjp/helpview.aspx?si=7087/file03612/math92.png)
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When converting to a function class, for example, Legendre, it is possible to request additional conversion rules to be performed. For instance, compare these two different outputs:
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