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Improve accuracy of asymptotic expansion for very large arguments (besselj, bessely) #37

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heltonmc opened this issue Aug 8, 2022 · 0 comments
Open

Improve accuracy of asymptotic expansion for very large arguments (besselj, bessely) #37

heltonmc opened this issue Aug 8, 2022 · 0 comments

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@heltonmc
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heltonmc commented Aug 8, 2022 •
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Right now, for very large arguments there are some roundoff errors when the argument is very large.

julia> Bessels.besseljy_large_argument(11, 2e9)
(-6.441564914025336e-6, 1.663779215046842e-5)

julia> Bessels.besseljy_large_argument(big"11", big"2e9")
(-6.441565416278640966871190587378818114705713999893782928810537933625658595387592e-06, 1.663779195601368418718142484679994485342917679346562260323801403887512758594912e-05)

It would be nice to improve the accuracy of these expansions.

Edit: Though it does look like it then improves...

julia> SpecialFunctions.besselj(11.0, 2e9)
-6.441565416278642e-6

julia> besselj(11.0, 2e9)
-6.441564914025336e-6

julia> besselj(11.0, 2e20)
4.600631613945902e-11

julia> SpecialFunctions.besselj(11.0, 2e20)
4.600631613945894e-11
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