besselJ(pi/2, sqrt(0.1)^(24:40))
[1] 4.720012e-01 4.720012e-01 4.720012e-01 4.720012e-01 4.720012e-01
1e-12 1e-13
1e-14
[6] 4.720012e-01 4.720012e-01 1.492599e+15 1.000000e+00 1.000000e+00
1e-15 1e-16
[11] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
1 e-17 1e-18
1e-19
[16] 1.000000e+00 1.000000e+00
1e-20
> besselJ(pi/1, 1E-15)
[1] -3.042422e+14
For what it's worth, the besselj function in Octave 8.4 doesn't do this.
octave:4> besselj(0.1.^(12:20), pi/2)
ans =
0.4720 0.4720 0.4720 0.4720 0.4720 0.4720 0.4720
0.4720 0.4720
Bessel functions are most commonly wanted at integer and half-integer orders,
so it's not surprising that a problem like this could go unnoticed for a while.
On Mon, 29 Dec 2025 at 05:29, Leo Mada via R-help <[email protected]> wrote:
>
> Dear R-Users,
>
> besselJ(pi/2, 0)
> # 0.4720012
> besselJ(pi/2, 1E-14)
> # 0.4720012
> besselJ(pi/2, 1E-15)
> # 4.720012e+14
>
> There seems to be an error in besselJ(pi/2, eps), where eps is close to 0;
> although besselJ(pi/2, 0) is well behaved.
>
> I am not an expert in the field - but it doesn't seem right.
>
> Sincerely,
>
> Leonard
>
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
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> PLEASE do read the posting guide https://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
______________________________________________
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PLEASE do read the posting guide https://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
