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convert/0F1

convert to special functions admitting a 0F1 hypergeometric representation

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

convert(expr, `0F1`)

Parameters

expr

-

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

Description

• 

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

FunctionAdvisor( `0F1` );

The 26 functions in the "0F1" class are particular cases of the hypergeometric function and are given by:

AiryAi,AiryBi,BesselI,BesselJ,BesselK,BesselY,HankelH1,HankelH2,KelvinBei,KelvinBer,KelvinHei,KelvinHer,KelvinKei,KelvinKer,cos,cosh,cot,coth,csc,csch,sec,sech,sin,sinh,tan,tanh

(1)
• 

convert/0F1 accepts as optional arguments all those described in convert/to_special_function.

Examples

1zaWhittakerM0,a,2IzΓ1+a2a2Iz12+a

zaWhittakerM0,a,2IzΓ1+a2a2Iz12+a

(2)

convert,`0F1`

zaBesselIa,IzIza

(3)

2a1πzaMeijerG,,0,a,1z24sinπ1+a+21+aπzaMeijerG,,0,a,1z24sinπa

2a1πzaMeijerG,,0,a,14z2sinπ1+a+21+aπzaMeijerG,,0,a,14z2sinπa

(4)

convert,`0F1`

2a1πBesselIa,z2asinπ1+a+21+aπzaBesselIa,zzasinπa2a

(5)

LaguerreL12a,2a,2IzWhittakerM0,a,2Iz

LaguerreL12a,2a,2IzWhittakerM0,a,2Iz

(6)

convert,`0F1`

2aΓ1+abinomial12+a,12aⅇIz2Iz12+aBesselIa,IzIza

(7)

See Also

convert

convert/`1F1`

convert/`2F1`

convert/to_special_function

FunctionAdvisor