math: add tests for corner cases of Yn Bessel function

[griesemer]

Follow-up on #18823 and corresponding change https://go-review.googlesource.com/#/c/35970/ (see Rob's comment in that change).

[alexd765]

I think we are already testing almost all the edge cases here.

We are testing Yn(n,a) for combinations of n=2,-3 and a= positive finite number, 0, -Inf, +Inf, NaN.
So it might be enough to add a = negative finite number and as a single special case Yn(0,0).

[gopherbot]

CL https://golang.org/cl/37310 mentions this issue.

[nerdatmath]

The special cases listed for Yn are:

Yn(n, +Inf) = 0
Yn(n ≥ 0, 0) = -Inf
Yn(n < 0, 0) = +Inf if n is odd, -Inf if n is even
Yn(n, x < 0) = NaN
Yn(n, NaN) = NaN

also

Y0(+Inf) = 0
Y0(0) = -Inf
Y0(x < 0) = NaN
Y0(NaN) = NaN

and

Y1(+Inf) = 0
Y1(0) = -Inf
Y1(x < 0) = NaN
Y1(NaN) = NaN

[Note that Y0(x) = Yn(0, x) and Y1(x) = Yn(1, x)]

Yn(n, x) is already tested for n ∈ {0, 1, 2, -3} and x ∈ {+∞, -∞, 0, NaN}, covering each of the above cases at least once. There are also several test cases over the same values of n with finite x>0. Note that the tests for n=0 and n=1 actually test Y0 and Y1 but that's equivalent. The only test that might be seen as missing is finite x<0 but I don't think it's needed.

[alexd765]

I think we are in agreement about which which cases are already tested.

The only case not tested at all is negative finite number for which I added a test with -1. This a usefull addition imo.

Y0(0) is already tested, like you said. So with the extra test Yn(0,0) we are only testing that Yn is calling Y0 in that case. I could see that this is something we might not need.

[nerdatmath]

Oh, sorry, I missed that you had already sent a CL. I don't think that Yn(0, x) is needed unless we also need Yn(1, x) (and Jn(0, x) and Jn(1, x)). In my opinion the case Yn(n, x<0) is already covered by Yn(n, -Inf), so I don't think we actually need any change at all here. Nevertheless, extra tests aren't going to hurt.

Since a CL is already provided, should the HelpWanted label be removed from this issue?