convert/Legendre
convert special functions admitting 2F1 hypergeometric representation into Legendre functions
Calling Sequence
Parameters
Description
Examples
convert(expr, Legendre)
expr
-
Maple expression, equation, or a set or list of them
convert/Legendre converts, when possible, special functions admitting a 2F1 hypergeometric representation into Legendre functions. The Legendre functions are
FunctionAdvisor( Legendre );
The 2 functions in the "Legendre" class are:
LegendreP,LegendreQ
arccothz
convert,Legendre
LegendreQ0,1z+π−z−122z−1
z+112bz−112bΓa+1Γ1−b+aJacobiPa,−b,b,z
z+1b2Γa+1JacobiPa,−b,b,zz−1b2Γ1−b+a
Γa+1a−b−bΓ−b+1LegendrePa,b,zΓ1−b+a
MeijerG−12a−12b,12−12a−12b,,0,−12−a,−1z2
MeijerG−a2−b2,12−a2−b2,,0,−12−a,−1z2
2z1+a+bLegendreQa,b,z2bz+1b2z−1b2ⅇIbπ
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:
GegenbauerCa,12,z
LegendrePa,z
convert,Legendre,raise a
3+2azLegendrePa+1,za+1−a+2LegendrePa+2,za+1
See Also
convert
convert/to_special_function
FunctionAdvisor
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