Bug 22502 – Potential error where std.internal.math.gammafunction.betaIncompleteInv gives different results from Wolfram Alpha for parameters aa and bb being half integer and yy0 being 0.025.

So I was trying to match a table in this article (https://www.jstor.org/stable/2676784), in particular Table 5. which basically corresponds to betaIncompleteInverse(x+1/2,N-x+1/2,0.05/2). Using Wolfram Alpha I can match the table, but I am getting numbers which seem surprisingly off when using betaIncompleteInverse. For example: InverseBetaRegularized[0.05/2, 7+1/2, 1+1/2] == 0.546280678967585... and betaIncompleteInv(7+1/2,1+1/2,0.05/2) ~= 0.590384 So I did a few sanity checks using the test cases in the unittests in the file (https://github.com/dlang/phobos/blob/v2.098.0/std/internal/math/gammafunction.d). For example: InverseBetaRegularized[0.0109343152340992, 8, 10] == 0.2 just like betaIncompleteInv(8, 10, 0.010_934_315_234_099_2L) ~= 0.2 Based on that I think I am using the function correctly, it is still possible I am doing something wrong though. Using the program: ``` import std.mathspecial; import std.stdio; real jefferys(real x, real N, real alpha=0.05){ return betaIncompleteInverse(x+1/2,N-x+1/2,alpha/2); } int main(){ for(real N =7; N< 10; N++){ for(real x=1; x < N;x++){ writef("(%f,%f) %f\n", N,x,jefferys(x,N)); } } return 0; } ``` and Wolfram Alpha like (https://www.wolframalpha.com/input/?i=InverseBetaRegularized%5B0.05%2F2%2C+1%2B1%2F2%2C+7-1%2B1%2F2%5D), just varying the parameters and Table 5 from the article I linked I get: (N,x) Wolfram D Table 5 (7,1) 0.0158765... 0.004211.. 0.016 (7,2) 0.0647282... 0.043272.. 0.065 (7,3) 0.1388642... 0.118117.. 0.139 (7,4) 0.2345012... 0.222778.. 0.234 And so on. Sorry if this is just some kind of user error on my part.

`+1/2` adds a `0` integer. With `+0.5`, the results should match.

(In reply to kinke from comment #1) > `+1/2` adds a `0` integer. With `+0.5`, the results should match. Awesome, thank you! I figured I was doing something stupid.