convert/1F1
convert to special functions admitting a 1F1 hypergeometric representation
Calling Sequence
Parameters
Description
Examples
convert(expr, `1F1`)
expr
-
a Maple expression, equation, or a set or list of them.
convert/1F1 converts, when possible, hypergeometric, MeijerG, and special functions admitting a 0F1 hypergeometric representation into special functions admitting a 1F1 hypergeometric representation; that is, into one of
FunctionAdvisor( `1F1` );
The 20 functions in the "1F1" class are particular cases of the hypergeometric function and are given by:
CoulombF,CylinderD,CylinderU,CylinderV,Ei,FresnelC,FresnelS,Fresnelf,Fresnelg,Γ,HermiteH,KummerM,KummerU,LaguerreL,WhittakerM,WhittakerW,dawson,erf,erfc,erfi
convert/1F1 accepts as optional arguments all those described in convert/to_special_function.
BesselIa,Iz
convert,`1F1`
IzaLaguerreL−12−a,2a,2IzΓa+12a−12+a−12−aⅇIz
hypergeom,c,z
LaguerreL12−c,−2+2c,4zc−3212−cⅇ2z
MeijerG,,12a,−12a,,14z2
MeijerG,,a2,−a2,,z24
ΓaLaguerreL−12+a,−2a,2zz24a2−12−a−12+aⅇz+Γ−az24a2LaguerreL−12−a,2a,2z−12+a−12−aⅇz
BesselJa,z+KelvinBeia−1,z−1
zaLaguerreL−12−a,2a,2IzΓa+12a−12+a−12−aⅇIz−Iⅇ12+I2z−12−12+I2z−12a−1LaguerreL12−a,−2+2a,−1−Iz−12Γa−32+a12−a2a+I−12−I2z−12a−1LaguerreL12−a,−2+2a,−1+Iz−12ⅇ12−I2z−12Γa−32+a12−a2a
See Also
convert
convert/`0F1`
convert/`2F1`
convert/to_special_function
FunctionAdvisor
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