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convert/Bessel_related

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

 

Calling Sequence

Parameters

Description

Examples

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,1z24GAMMA1+a2a

zahypergeom,1+a,z24Γ1+a2a

(2)

convert,Bessel_related

BesselJa,z

(3)

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

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

(4)

convert,Bessel_related

a1212aⅇIzΓ1+aBesselJa,z2aza2Iz12+aΓ1+aBesselJa,z2aza

(5)

KummerUa+12,2a+1,z

KummerU12+a,2a+1,z

(6)

convert,Bessel_related

πⅇz2BesselJa,I2zI2za22a+14z2a2a+BesselJa,I2z2a4I2za22a1sinπ1+a

(7)

MeijerG,,1a2,1a2,z

MeijerG,,a2,a2,z

(8)

convert,Bessel_related

za2BesselJa,2z2a2za

(9)

See Also

convert

convert/to_special_function

convert[Airy]

convert[Bessel]

convert[Hankel]

convert[Kelvin]

FunctionAdvisor