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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+12abinomial12+a,12aⅇIz

(3)

hypergeom,c,z

hypergeom,c,z

(4)

convert,`1F1`

LaguerreL12c,2+2c,4zbinomialc32,12cⅇ2z

(5)

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

MeijerG,,12a,12a,,14z2

(6)

convert,`1F1`

ΓaLaguerreL12+a,2a,2z14z212abinomial12a,12+aⅇz+Γa14z212aLaguerreL12a,2a,2zbinomial12+a,12aⅇz

(7)

BesselJa,z+KelvinBeia1,z1

BesselJa,z+KelvinBeia1,z1

(8)

convert,`1F1`

zaLaguerreL12a,2a,2IzΓa+12abinomial12+a,12aⅇIzIⅇ12+12Iz1212+12Iz12a1LaguerreL12a,2a2,1Iz12Γabinomial32+a,12a2a+I1212Iz12a1LaguerreL12a,2a2,1+Iz12ⅇ1212Iz12Γabinomial32+a,12a2a

(9)

See Also

convert

convert/`0F1`

convert/`2F1`

convert/to_special_function

FunctionAdvisor