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convert/Kummer

convert special functions admitting 1F1 or 0F1 hypergeometric representation into Kummer functions

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

convert(expr, Kummer)

Parameters

expr

-

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

Description

• 

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

FunctionAdvisor( Kummer );

The 2 functions in the "Kummer" class are:

KummerM,KummerU

(1)

Examples

AiryAiz

AiryAiz

(2)

convert,Kummer

313KummerM16,13,4z3233Γ23z316Γ23KummerM56,53,4z3232πⅇ2z323

(3)

HermiteHa,zLaguerreL2,ⅇz

HermiteHa,zLaguerreL2,ⅇz

(4)

convert&comma;Kummerassuming0<&real;z

2aπKummerMa2&comma;12&comma;z2Γ12a22zKummerM12a2&comma;32&comma;z2Γa2KummerM−2&comma;1&comma;KummerM1&comma;1&comma;z

(5)

&ExponentialE;zerfz2&plus;WhittakerW1&comma;12&comma;z&ExponentialE;1z2MeijerG1a&comma;&comma;0&comma;1b&comma;&comma;1zBesselK3&comma;1z

&ExponentialE;zerfz2+WhittakerW−1&comma;12&comma;z&ExponentialE;z2MeijerG1a&comma;&comma;0&comma;1b&comma;&comma;1zBesselK3&comma;1z

(6)

convert&comma;Kummer

2KummerM1&comma;1&comma;zz2KummerM12&comma;32&comma;z4π+KummerU2&comma;2&comma;zzKummerM1&comma;1&comma;z2&ExponentialE;z2ΓaΓ1bKummerMa&comma;b&comma;1z+KummerM1+ab&comma;2b&comma;1zΓ1+abΓ1+b1z1+bπ22z3KummerU72&comma;7&comma;22z&ExponentialE;1+z

(7)

See Also

convert

convert/to_special_function

FunctionAdvisor