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

(6)

convert,`2F1`

Γa+32Γa2b2JacobiPa21b2,a+12,b,z22z2Γa2+12b2

(7)

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

hypergeoma,b+c+a+1,1+b,12z2

(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

MeijerGa2b2,12a2b2,,0,a12,1z2

(14)

convert,`2F1`

πΓ1+a2+b2JacobiP12a2b2,a+12,b,z22z2Γa2+1b2sinπa+b+12

(15)

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

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

(16)

convert,`2F1`

πcscπa1+zb2LegendrePa,b,z1+zb2

(17)

See Also

convert

convert/`0F1`

convert/`1F1`

convert/to_special_function

FunctionAdvisor