convert/Kummer
convert special functions admitting 1F1 or 0F1 hypergeometric representation into Kummer functions
Calling Sequence
Parameters
Description
Examples
convert(expr, Kummer)
expr
-
Maple expression, equation, or a set or list of them
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
AiryAiz
convert,Kummer
313KummerM16,13,4z3233Γ23−z316Γ23KummerM56,53,4z3232πⅇ2z323
HermiteHa,zLaguerreL2,expz
HermiteHa,zLaguerreL2,ⅇz
convert,Kummerassuming0<ℜz
2aπKummerM−a2,12,z2Γ12−a2−2zKummerM12−a2,32,z2Γ−a2KummerM−2,1,KummerM1,1,z
expzerfz2+WhittakerW−1,12,zexp12zMeijerG1−a,,0,1−b,,1zBesselK−3,1−z
ⅇzerfz2+WhittakerW−1,12,zⅇz2MeijerG1−a,,0,1−b,,1zBesselK3,1−z
2KummerM1,1,zz2KummerM12,32,−z4π+KummerU2,2,zzKummerM1,1,z2ⅇz2ΓaΓ1−bKummerMa,b,1z+KummerM1+a−b,2−b,1zΓ1+a−bΓ−1+b1z−1+b8π1−z3KummerU72,7,2−2zⅇ−1+z
See Also
convert
convert/to_special_function
FunctionAdvisor
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