convert/Whittaker
convert special functions admitting 1F1 or 0F1 hypergeometric representation into Whittaker functions
Calling Sequence
Parameters
Description
Examples
convert(expr, Whittaker)
expr
-
Maple expression, equation, or a set or list of them
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
AiryAiz
convert,Whittaker
3WhittakerM0,−13,4z32345612Γ23z3216−3zΓ23WhittakerM0,13,4z3234168πz3256
HermiteHa,zLaguerreL2,expz
HermiteHa,zLaguerreL2,ⅇz
convert,Whittakerassuming0<ℜz
2aπⅇz22WhittakerMa2+14,−14,z2z214Γ12−a2−2zWhittakerMa2+14,14,z2z234Γ−a2WhittakerM52,0,WhittakerM−1,12,zⅇz2zⅇWhittakerM−1,12,zⅇz22zWhittakerM−1,12,zⅇz2z
expzerfz2+KummerU−1,12,zexp12zMeijerG1−a,,0,1−b,,1zBesselK−3,1−z
ⅇzerfz2+KummerU−1,12,zⅇz2MeijerG1−a,,0,1−b,,1zBesselK3,1−z
2WhittakerM−1,12,zⅇz2zWhittakerM14,14,−z4πⅇz42−z434+2WhittakerW54,−14,zⅇz2WhittakerM−1,12,z2ⅇz4z54ⅇ12zΓaΓ1−bWhittakerM−a+b2,b2−12,1z+WhittakerM−a+b2,12−b2,1zΓ1+a−bΓ−1+b2−2z1zb2πWhittakerW0,3,2−2z
See Also
convert
convert/to_special_function
FunctionAdvisor
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