convert special functions admitting 1F1 or 0F1 hypergeometric representation into Bessel related functions - Maple Help

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convert/Bessel_related - convert special functions admitting 1F1 or 0F1 hypergeometric representation into Bessel related functions

Calling Sequence

convert(expr, Bessel_related)

Parameters

expr

-

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

Description

• 

convert/Bessel_related converts, when possible, special functions admitting a 1F1 or 0F1 hypergeometric representation into Bessel related functions. The Bessel related functions are

FunctionAdvisor( Bessel_related );

The 14 functions in the "Bessel_related" class are:

AiryAi,AiryBi,BesselI,BesselJ,BesselK,BesselY,HankelH1,HankelH2,KelvinBei,KelvinBer,KelvinHei,KelvinHer,KelvinKei,KelvinKer

(1)

Examples

1zahypergeom,1+a,1z24Γ1+a2a

zahypergeom,1+a,14z2Γ1+a2a

(2)

convert,Bessel_related

BesselJa,z

(3)

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

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

(4)

convert,Bessel_related

binomiala12,12aⅇIzΓ1+aBesselJa,z2aza2Iz12+aΓ1+aBesselJa,z2aza

(5)

KummerUa+12,2a+1,z

KummerU12+a,1+2a,z

(6)

convert,Bessel_related

πⅇ12z14BesselJa,12Iz12Iza21+2az2a2a+14BesselJa,12Iz2a12Iza22a1sinπ1+a

(7)

MeijerG,,1a2,1a2,z

MeijerG,,12a,12a,z

(8)

convert,Bessel_related

z12aBesselJa,2z2a2za

(9)

See Also

convert, convert/to_special_function, convert[Airy], convert[Bessel], convert[Hankel], convert[Kelvin], FunctionAdvisor


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