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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

3WhittakerM0,13,4z32345612Γ23z32163zΓ23WhittakerM0,13,4z3234168πz3256

(3)

HermiteHa,zLaguerreL2,ⅇz

HermiteHa,zLaguerreL2,ⅇz

(4)

convert&comma;Whittakerassuming0<&real;z

2aπWhittakerMa2+14&comma;14&comma;z2&ExponentialE;z22z214Γ12a22zWhittakerMa2+14&comma;14&comma;z2&ExponentialE;z22z234Γa2WhittakerM52&comma;0&comma;WhittakerM−1&comma;12&comma;z&ExponentialE;z2z&ExponentialE;WhittakerM−1&comma;12&comma;z&ExponentialE;z22zWhittakerM−1&comma;12&comma;z&ExponentialE;z2z

(5)

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

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

(6)

convert&comma;Whittaker

2WhittakerM−1&comma;12&comma;z&ExponentialE;z2zWhittakerM14&comma;14&comma;z4π&ExponentialE;z42z434+2WhittakerW54&comma;14&comma;z&ExponentialE;z2WhittakerM−1&comma;12&comma;z2&ExponentialE;z4z54&ExponentialE;12zΓaΓ1bWhittakerMa+b2&comma;b212&comma;1z+WhittakerMa+b2&comma;12b2&comma;1zΓ1+abΓ1+b22z1zb2πWhittakerW0&comma;3&comma;22z

(7)

See Also

convert

convert/to_special_function

FunctionAdvisor