convert/2F1 - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Conversions : Function Class : convert/`2F1`

convert/2F1

convert to special functions admitting a 2F1 hypergeometric representation

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

convert(expr, `2F1`)

Parameters

expr

-

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

Description

• 

convert/2F1 converts, when possible, hypergeometric / MeijerG functions into special functions admitting a 2F1 hypergeometric representation; that is, into one of

FunctionAdvisor( `2F1` );

The 26 functions in the "2F1" class are particular cases of the hypergeometric function and are given by:

ChebyshevT,ChebyshevU,EllipticCE,EllipticCK,EllipticE,EllipticK,GaussAGM,GegenbauerC,JacobiP,LegendreP,LegendreQ,LerchPhi,SphericalY,arccos,arccosh,arccot,arccoth,arccsc,arccsch,arcsec,arcsech,arcsin,arcsinh,arctan,arctanh,ln

(1)
• 

convert/2F1 accepts as optional arguments all those described in convert/to_special_function.

Examples

zhypergeom12,1,32,z2

zhypergeom12,1,32,z2

(2)

convert,`2F1`

arctanhz

(3)

hypergeom12,12,1,z2

hypergeom12,12,1,z2

(4)

convert,`2F1`

JacobiP12,0,1,2z2+1

(5)

hypergeom1a2+1b2+12,1+1a2+1b2,a+32,1z2

hypergeom1+12a+12b,12a+12b+12,a+32,1z2

(6)

convert,`2F1`

Γa+32Γ12a12bJacobiP12a112b,a+12,b,z22z2Γ12a+1212b

(7)

hypergeomb+c+a+1,a,1+b,121z2

hypergeoma,b+c+a+1,1+b,1212z

(8)

convert,`2F1`

Γ1+bΓa+1JacobiPa,b,c,zΓa+b+1

(9)

MeijerG0,12,,0,12,1z2

MeijerG0,12,,0,12,1z2

(10)

convert,`2F1`

2zarctanh1z

(11)

MeijerG12,12,,0,0,1+z2

MeijerG12,12,,0,0,z21

(12)

convert,`2F1`

πGegenbauerC12,12,2z21

(13)

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

MeijerG12a12b,1212a12b,,0,a12,1z2

(14)

convert,`2F1`

πΓ1+12a+12bJacobiP1212a12b,a+12,b,z22z2Γ12a+112bsin12πa+b+1

(15)

MeijerGa,a+1,,0,b,12+1z2

MeijerGa,a+1,,0,b,12+12z

(16)

convert,`2F1`

πcscπa1+z12bLegendrePa,b,z1+z12b

(17)

See Also

convert

convert/`0F1`

convert/`1F1`

convert/to_special_function

FunctionAdvisor