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convert/1F1

convert to special functions admitting a 1F1 hypergeometric representation

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

convert(expr, `1F1`)

Parameters

expr

-

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

Description

• 

convert/1F1 converts, when possible, hypergeometric, MeijerG, and special functions admitting a 0F1 hypergeometric representation into special functions admitting a 1F1 hypergeometric representation; that is, into one of

FunctionAdvisor( `1F1` );

The 20 functions in the "1F1" class are particular cases of the hypergeometric function and are given by:

CoulombF,CylinderD,CylinderU,CylinderV,Ei,FresnelC,FresnelS,Fresnelf,Fresnelg,Γ,HermiteH,KummerM,KummerU,LaguerreL,WhittakerM,WhittakerW,dawson,erf,erfc,erfi

(1)
• 

convert/1F1 accepts as optional arguments all those described in convert/to_special_function.

Examples

BesselIa,Iz

BesselIa,Iz

(2)

convert,`1F1`

IzaLaguerreL12a,2a,2IzΓa+12a12+a12aⅇIz

(3)

hypergeom,c,z

hypergeom,c,z

(4)

convert,`1F1`

LaguerreL12c,2+2c,4zc3212cⅇ2z

(5)

MeijerG,,1a2,1a2,,1z24

MeijerG,,a2,a2,,z24

(6)

convert,`1F1`

ΓaLaguerreL12+a,2a,2zz24a212a12+aⅇz+Γaz24a2LaguerreL12a,2a,2z12+a12aⅇz

(7)

BesselJa,z+KelvinBeia1,z1

BesselJa,z+KelvinBeia1,z1

(8)

convert,`1F1`

zaLaguerreL12a,2a,2IzΓa+12a12+a12aⅇIzIⅇ12+I2z1212+I2z12a1LaguerreL12a,2+2a,−1Iz12Γa32+a12a2a+I12I2z12a1LaguerreL12a,2+2a,−1+Iz12ⅇ12I2z12Γa32+a12a2a

(9)

See Also

convert

convert/`0F1`

convert/`2F1`

convert/to_special_function

FunctionAdvisor