convert/Kelvin
convert special functions admitting 1F1 or 0F1 hypergeometric representation into Kelvin functions
Calling Sequence
Parameters
Description
Examples
convert(expr, Kelvin)
expr
-
Maple expression, equation, or a set or list of them
convert/Kelvin converts, when possible, special functions admitting a 1F1 or 0F1 hypergeometric representation into Kelvin functions. The Kelvin functions are
FunctionAdvisor( Kelvin );
The 6 functions in the "Kelvin" class are:
KelvinBei,KelvinBer,KelvinHei,KelvinHer,KelvinKei,KelvinKer
AiryAiz
convert,Kelvinassuming0<ℜz
3zKelvinKer13,13−I3z322+IKelvinKei13,13−I3z3223+I6π
Consider the following expression
sol≔yz=_C1KummerM12+a,1+2a,z+_C2KummerU12+a,1+2a,z
where sol is the solution to the following linear differential equation (see dpolyform)
PDEtoolsdpolyformsol,no_Fn
ⅆ2ⅆz2yz=−2a+z−1ⅆⅆzyzz+1+2ayz2zwhere
sol can be rewritten using Kelvin functions
convertsol,Kelvin
yz=c__1ⅇz2Γ1+aKelvinBera,14−I4z2+IKelvinBeia,14−I4z22aI2za+c__2πⅇz22aKelvinBera,14−I4z2I2za2−1+2a−I2za21+2aKelvinBer−a,14−I4z2z2a2a−IKelvinBei−a,14−I4z2I2za21+2az2a2a+IKelvinBeia,14−I4z22aI2za2−1+2a4sinπ1+a
collect,KelvinBer,KelvinBei,simplify
yz=ⅇz2Iz−a24ac__1Γ1+a−c__2πcscπaKelvinBera,14−I4z22+c__2z−2aπIzaⅇz2cscπaKelvinBer−a,14−I4z22+IIz−aⅇz24ac__1Γ1+a−c__2πcscπa2KelvinBeia,14−I4z2+Ic__2z−2aπIzaⅇz2cscπaKelvinBei−a,14−I4z22
See Also
convert
convert/to_special_function
FunctionAdvisor
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