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convert/Hankel

convert special functions admitting 1F1 or 0F1 hypergeometric representation into Hankel (Bessel of third kind) functions

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

convert(expr, Hankel)

Parameters

expr

-

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

Description

• 

convert/Hankel converts, when possible, special functions admitting a 1F1 or 0F1 hypergeometric representation into Hankel (Bessel of third kind) functions. The Hankel functions are

FunctionAdvisor( Hankel );

The 2 functions in the "Hankel" class are:

HankelH1,HankelH2

(1)

Examples

BesselJa,z

BesselJa,z

(2)

convert,Hankel

12HankelH1a,z+12HankelH2a,z

(3)

BesselKa,z

BesselKa,z

(4)

convert,Hankel

Iza2ⅇIaπ+Iza2ⅇ2IaπHankelH1a,Iz+Iza2za2ⅇIaπHankelH2a,IzπIzaza2ⅇ2Iaπ2

(5)

KummerUa+12,2a+1,z

KummerUa+12,2a+1,z

(6)

convert,Hankel

18ⅇIaπ12Iza22a+1z2a2a+182a12Iza21+2aHankelH1a,12Iz+1812Iza22a+1z2aⅇIaπ2a+182a12Iza21+2aHankelH2a,12Izπⅇ12zsinπa+1

(7)

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

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

(8)

convert,Hankel

12binomiala12,12aⅇIzΓa+1HankelH1a,z+HankelH2a,z2aza122Iza+12Γa+1HankelH1a,z+HankelH2a,z2aza

(9)

MeijerG,,1a2,1a2,z

MeijerG,,12a,12a,z

(10)

convert,Hankel

12z12aHankelH1a,2z+HankelH2a,2z2a2za

(11)

See Also

convert

convert/to_special_function

FunctionAdvisor

 


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