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convert/Legendre

convert special functions admitting 2F1 hypergeometric representation into Legendre functions

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

convert(expr, Legendre)

Parameters

expr

-

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

Description

• 

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

(1)

Examples

arccothz

arccothz

(2)

convert,Legendre

LegendreQ0,1z+12πz12z1

(3)

z+11b2Γa+1JacobiPa,b,b,zz11b2Γ1b+a

z+112bΓa+1JacobiPa,b,b,zz112bΓ1b+a

(4)

convert,Legendre

Γa+1binomialb+a,bΓb+1LegendrePa,b,zΓ1b+a

(5)

MeijerG1a21b2,121a21b2,,0,12a,1z2

MeijerG12a12b,1212a12b,,0,12a,1z2

(6)

convert,Legendre

2z1+a+bLegendreQa,b,z2bz+112bz112bⅇIbπ

(7)

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

GegenbauerCa,12,z

(8)

convert,Legendre

LegendrePa,z

(9)

convert,Legendre,raise a

3+2azLegendrePa+1,za+1a+2LegendrePa+2,za+1

(10)

See Also

convert

convert/to_special_function

FunctionAdvisor

 


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