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convert/Whittaker

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

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

convert(expr, Whittaker)

Parameters

expr

-

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

Description

• 

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

FunctionAdvisor( Whittaker );

The 2 functions in the "Whittaker" class are:

WhittakerM,WhittakerW

(1)

Examples

AiryAiz

AiryAiz

(2)

convert,Whittaker

1123WhittakerM0,13,43z3/245/6Γ23z3/21/638zΓ23WhittakerM0,13,43z3/241/6πz3/25/6

(3)

HermiteHa,zLaguerreL2,ⅇz

HermiteHa,zLaguerreL2,ⅇz

(4)

convert&comma;Whittakerassuming0<&real;z

2a&pi;WhittakerM12a&plus;14&comma;14&comma;z2&ExponentialE;12z2z21&sol;4&Gamma;1212a2zWhittakerM12a&plus;14&comma;14&comma;z2&ExponentialE;12z2z23&sol;4&Gamma;12aWhittakerM52&comma;0&comma;WhittakerM0&comma;12&comma;z&ExponentialE;12z&ExponentialE;12WhittakerM0&comma;12&comma;z&ExponentialE;12zWhittakerM0&comma;12&comma;z&ExponentialE;12z

(5)

&ExponentialE;zerfz2&plus;KummerU1&comma;12&comma;z&ExponentialE;1z2MeijerG1a&comma;&comma;0&comma;1b&comma;&comma;1zBesselK3&comma;1z

&ExponentialE;zerfz2&plus;KummerU1&comma;12&comma;z&ExponentialE;12zMeijerG1a&comma;&comma;0&comma;1b&comma;&comma;1zBesselK3&comma;1z

(6)

convert&comma;Whittaker

2WhittakerM0&comma;12&comma;z&ExponentialE;12zz2WhittakerM14&comma;14&comma;z4&pi;&ExponentialE;12z4z43&sol;4&plus;WhittakerW54&comma;14&comma;z&ExponentialE;12zWhittakerM0&comma;12&comma;12z&ExponentialE;14zz1&sol;4&ExponentialE;12z&Gamma;a&Gamma;1bWhittakerMa&plus;12b&comma;12b12&comma;1z&plus;WhittakerMa&plus;12b&comma;1212b&comma;1z&Gamma;1&plus;ab&Gamma;1&plus;b22z1z12b&pi;WhittakerW0&comma;3&comma;22z

(7)

See Also

convert

convert/to_special_function

FunctionAdvisor

 


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