convert/Kummer - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Conversions : Function Class : convert/Kummer

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

1331/3KummerM16,13,43z3/2Γ2312z31/6Γ23KummerM56,53,43z3/2πⅇ23z3/2

(3)

HermiteHa,zLaguerreL2,ⅇz

HermiteHa,zLaguerreL2,ⅇz

(4)

convert&comma;Kummerassuming0<&real;z

2a&pi;KummerM12a&comma;12&comma;z2&Gamma;1212a2zKummerM1212a&comma;32&comma;z2&Gamma;12aKummerM2&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&plus;WhittakerW1&comma;12&comma;z&ExponentialE;12zMeijerG1a&comma;&comma;0&comma;1b&comma;&comma;1zBesselK3&comma;1z

(6)

convert&comma;Kummer

2KummerM1&comma;1&comma;zz2KummerM12&comma;32&comma;z4&pi;&plus;KummerU2&comma;2&comma;zzKummerM1&comma;1&comma;12z&ExponentialE;12z&Gamma;a&Gamma;1bKummerMa&comma;b&comma;1z&plus;KummerM1&plus;ab&comma;2b&comma;1z&Gamma;1&plus;ab&Gamma;1&plus;b1z1&plus;b&pi;22z3KummerU72&comma;7&comma;22z&ExponentialE;1&plus;z

(7)

See Also

convert

convert/to_special_function

FunctionAdvisor

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam